
Qass 
Book 



METHOD IN 



Reading and Number. 



BY 

GEO. yV. NEET. 

Professor of Pejdagoqy iisr the Northern 

Indiana Normal School, 

VALPARAISO, iNr>. 



M. E. BOQARTE, PUBLISHER, 

VALPARAISO, INDIANA. 
lOOO. 



Librwrv of Conarc«9 

JAN 30 1901 

Copy^g^t ftotry 

SECOND COPY 



^ 



COPYRIGHT 1900, 
By GEO. W. NEET. 



PREFACE. 

These studies in method in reading and number 
are born of a desire to help the students in the 
writer's own classes in method in these subjects. 
There are many students who appreciate the neces- 
sity of the study of method in reading and number, 
and who are earnestly seeking help along the lines of 
a better method of teaching these subjects than that 
in use in many places. To give guidance to these 
students is the main idea which prompted to the 
preparation of these studies. 

A second thought is, that many fellow teachers 
who have not had the time nor opportunity to make 
special studies in method in reading and number may 
receive help and guidance from these studies. 

It is the aim of the present discussion (1) to 
investigate the theory aspect of method in reading 
and number in the light of the best educational 
thought of to-day; (2) to give an abundance of con- 
crete illustrations of what these lessons should be in 
harmony with the theory; (3) to criticise existing 
practices in the teaching of reading and number 
which are thought to be bad. Thus the studies are 
theoretical, practical, and critical. 



IV. PREFACE. 

Simplicity and definiteness have been aimed at 
through the entire discussion to the end that direct 
help might be given to those who are beginning teach- 
ers in these subjects. 

These studies are believed to be in harmony with 
the best educational thought of the present times. 

So far as known no other definite and simple dis- 
cussion of method in these subjects is in print. 

G. W. N. 



CONTENTS. 
CHAPTER I. 



General Method, . . . . q_^i 

The Teaching Act, - - - - 9 

The Processes in It, - - - 9 

Nature of Method as a Subject, - - - 10-11 

Classes of Method, _ . _ _ yL 

The Learner's Method, - - - - 11-13 

The Teacher's Method, - - - 13-20 

Method as a Physical Process, - - 20-25 

Comparison of Teacher's and Pupil's Method, 29-30 

Two Views of Method, - - . . 26-28 

No Danger in Too Much Study of Method, - 29-30 

Factors Determining Method, - - ' - 30-31 

CHAPTER II. 

The Purpose of Reading, - - - 32-38 

General Meaning, . - . _ _ 32 

Importance of Definite Idea of Purpose, - 32-33 

Classes of Purposes, or Aims, - - 33 

The Main, or Primary, Aim, - - 33-35 

' Evidence of Main Aim, - - - 35 

Secondary, or Subordinate, Aim, - 36-37 

Relation of These Aims, . _ _ 37 

The Purpose of Reading and Literature, - 38 

CHAPTER III. 

Nature of Reading as a Subject, - 39-43 

The School Curriculum, - - - . 39 

The Language Group, - - _ . _ 39-40 

The Subject-matter of Reading, - - - 41-42 

Definition of Reading, - . . - 42-43 

CHAPTER IV. 

Procedure in Teaching Reading, - 44-74 

Stages of Reading, - ... 44 



VI. 



CONTENTS. 



The Preparatory Stage, 

The Stage of Reading Proper, 

The Starting Point, - - - - 

Basis, - - 

The First Unknown, - _ . . - 

Methods of Beginning, . - . . 

The Alphabet Method, - . . . 

The Synthetic Method, . . _ 

The Sentence Method, . - _ 
The Analytic Word Method, 

Definite Procedure, - - - - - 

Adjectives, and Action Words, 
The, A, An, Is, Can, On, In, etc., 
Fixing the Vocabulary in Mind, 
Print and Script, _ - . . . 

Reading of Simple Pieces of Discourse, 
Analysis Work, . _ . - 

Working Out New Words as to Pronunciation, 
Diacritical Marks, . . - - 



44-45 
45-46 

46 
46-47 

47 

47-48 
48-50 
50-54 
54-56 
66-57 

57-60 

60 

60-61 

61 

62 

62-63 

63-66 

66-68 

68 

68-69 
69-70 
70-72 
72-73 

73-74 



Second Stage, - - 

Didactic and Symbolic Discourse, 
Steps in Symbolic Discourse, 
Steps in Didactic Discourse, - 

Summary, ----- 
CHAPTER V. 
Concrete Illustrations, 

Advantage of, - - - - 

Excelsior, . - - . 

Erastus Wren's Virtue, - - 

The Golden Touch, 

Orchard Life, . - - 

Abou Ben Adhem, - - - 

CHAPTER VI. 
Common Errors in Teaching Reading, - 89-92 

Opportunities for, ----- 89 

The Use of the Alphabet Method, - - 89-90 

Phonetic Work, or Sound Analysis, - - 90 

Oral Reading to the Exclusion of Interpretation, 90-91 

Lack of Thought Interpretation, - - 91 

Indefinite, General Assignments, - - - 92 



75-88 

75 

75-79 

80-81 

82-86 

87-88 

88 



CONTENTS. VII. 

CHAPTER VII. 

Supplementary Reading, - - - 93-98 

Nature of, ----- - 93 

Need and Value of, - - - _ _ 93 

A Difficulty, ---... 93 

Lists of Books, - - - . - 94-98 

CHAPTER VIII. 

Nature and Origin of Number, - 99-106 

Nature of Number, . . _ _ 99-IOI 

Genesis of Number, - - - - - 101-102 

Definition of Number, - - . . 102-103 

Origin of Number, - - - - - 103 

Limitation, - - - - . _ 103-105 

Conclusions, - - - - - . 105-106 

CHAPTER IX. 

Method op Procedure in Teaching Number, 

107-131 

Points to Be Kept in Mind, - - - 107 

Methods in Use, - - . . . 108 

The Method of Symbols, - - - 108-109 

The Fixed Unit Method, - - - 109-112 

The Grube Method, - - - - 112-113 

The Speer Method, - - - - 113-116 

The Practical Method, - . - . 117 

Two Stag-es of Number Work, - - - 117-118 

Characteristics of Primary Stage, - - 118 

Scope of Work in Primary Stage, - - 118-121 

What Can Be Known of a Number, - - 121-124 

What to Do with a Number in the Primary Stage, 124 

The Number as a Whole, - - - 124 

The One, the Measuring Unit, - - - 125-126 

The Relations in the Number, - - 126-128 

The Applications of a Numbef , - - - 128-130 

Notation of the Number, - - - 130-131 

CHAPTER X. 

Method of Procedure in Teaching Number, — 

Concluded, - - - 132-153 

The Primary Stage, .... 132-135 

The Number as a Whole, - - - - 135-136 

The Relations in a Number, - - - 136-138 



vnii 



CONTENTS. 



Thoroughness of Work, - 

Fractional Relations, 

Important and Unimportant Relations, 

The General A])plications, 

Picturing Problems, 

Notation, _ . - - 

Enumeration, _ . . . 

The Multiplication Table, 

Teachers' Helps, 

CHAPTER XI. 
Procedure in Second Stage, 

General Scope, 

The Formal Process of Addition, 

The Formal Process of Subtraction, - 

The Formal Process of Multiplication, 

The Formal Process of Division, 

Conclusion, . _ - _ 



138-139 
139-141 
141-142 
142-144 
144 145 
145-150 
150 
150-152 
152-153 



154-164 

154 
154-156 
156-159 
159-161 
161-164 

164 



CHAPTER XII. 

The Subject-matter and Purpose of Number, 

165-170 

- 165-166 
166 

- 166-167 



General Nature of Subject-matter, 
The Purpose of Number, - - - 

The Knowledge-giving Purpose, 
The Guidance the Knowledge of Number 

Gives, . - - - 

The Disciplinary Purpose, 
Conclusions, - - 

CHAPTER XIII. 



167-169 

169-170 

170 



Common Errors in Teaching Number, - 171-179 



Prevalence of, - - - 

Wrong Number Concepts, 
Figures instead of Number, 
Unsystematic Number Teaching, 
Teaching from the Form Side, 
Failure to Picture Problems, 
Exhausting a Number, 
Relations among Topics, 
Thoughts of Others, 

Conclusion, - - - - 



171-172 
172 
173 

173-174 
174 

174-175 
175 

175-176 

176-179 
179 



CHAPTER I. 

GENERAL METHOD. 

The Teaching Act. — The school exists as an organ- 
ization in order that the most favorable conditions 
may be furnished for the act of teaching. It is in 
this act that the mind of the pupil comes into vital 
touch with the mind of the teacher. Here the miracle 
of the influence of one mind upon another is mani- 
fested. Here it is that an ^U-important duty of the 
teacher is involved. To this process all other pro- 
cesses of the school point. The school finds the idea 
that created it in the process of realization in the 
teaching act. The act of teaching is a process for it 
is a series of steps directed toward the accomplish- 
ment of an end. The teaching act is not a simple 
process for it is a large process made up of smaUer 
processes. 

The Processes in It. — A brief analysis of the teach- 
ing act will show that there are three processes going 
on in it, — (1) the thinking the learner is doing; (2) the 
thinking the teacher is doing; (3)-a process of hand- 
ling questions, directions, objects, assignments, and 
so on — the manipulation of means in teaching. The 
first two of these processes are spiritual, or mental, 



10 METHOD IN READING AND NUMBER. 

processes, and the third is external to the minds of 
both the teacher and the pupil and is a physical pro- 
cess. 

Illustration. — In teaching the definition of a noun 
to a student, first, the student's mind goes through 
the process of thinking (1) that the noun is a sub- 
stantive word; and (!?) that it expresses an object by- 
naming it. This is the process in the mind of the 
student in the teaching act. Secondly, the teacher 
thinks these same points through with the student, 
but he thinks several other things, too. This is the 
spiritual process of the teacher in the teaching act. 
Thirdly, there is a process of asking questions, an- 
swering questions, illustrating, possibly referring to 
text-books, etc., going on, and this is the physical 
process in the teaching act. 

Nature of Method as a Subject of Study. — The ques- 
tion. What is the subject of method like? is often 
asked. It may be answered in a general way by say- 
ing it is a subject of study the pursuit of which has 
for its special object to make teachers more skillful 
in teaching than they would be without such study. 
But this much might be said of any pedagogical study 
— of psychology, for instance. To be more definite, 
method as a subject is that study which deals with 
the three processes in the act of teaching as indicated 
above. These three processes in their various phases 
constitute the material of all study in the subject of 
method. 



METHOD IN READING AND NUMBER. 11 

The Subject-matter of Method. — By subject-matter 
is meant the '.material of study in any subject or 
lesson. It is the thought and feehng embodied in 
any subject or lesson which are to be got from such 
subject or lesson by study. It always consists of 
facts and relations among such facts. So the sub- 
ject-matter of method, as a subject of study, is the 
three processes, one in the mind of the learner, one 
in the mind of the teacher, and one a physical pro- 
cess, in their relation to the growth in the life of the 
learner. 

Definition o/ife^Aod— Method is thus seen to be a 
complex and comprehensive thing. Any definition, 
to be perfectly accurate, must include the various 
phases of these three processes. The following, it 
seems, does this: Method is the triple process in the act 
of teaching hy ichich the learner is induced to take the 
steps from his real condition to a higher condition held 
up as an ideal. This is the definition of method con- 
sidered in its broadest and most comprehensive 
sense, and the sense in which its study will giv« the 
most help to the teacher. 

Classes of Method. — Since there are three pro- 
cesses going on in the teaching act there are, in a 
sense, three methods,^ — the learner's method, the 
teacher's method, and physical method. These three 
will be studied somewhat in detail. 

The Learner's Method. — The learner's method is 
the movement of his mind in gaining any point of 



12 METHOD IN READING AND NUMBER. 

knowledge. The pupil's method is thus a living, 
spiritual process internal to his life. Method from 
this point of view is mental growth. Tliat is to say, 
it is the change of potential mental activity into actual 
mental activity, and this is the essence of growth. 

Illustration. — If the child learns in a number 
lesson that 8+7 = 15, the activity of his mind in 
thinking the following steps is his method: — (1) The 
mind rethinks the number 8; (2) the mind rethinks 
the number 7; (3) the mind thinks the number 8 and 
the number 7 together; (4) the mind thinks the name 
of the new number. These four steps are the mind's 
process in thinking the point of knowledge, and are, 
therefore, the mind's method. This phase of method 
calls attention to the fact that the thing to be watched 
and emphasized in teaching is the change in the 
learner's life by which he is constantly rising to a 
higher plane of living. 

Definition of the Learner' s Method. — This phase of 
method may be characterized by the following defini- 
tions : — 

1. Method is the process in the learner's mind 
in thinking a thing. 

2. Method is the movement by which the mind 
of the learner identifies itself with the thought and 
feeling of the external world. The external world 
here means anything external to the mind of the 
learner. 

3. Method is the mental activity in which the 



METHOD IN READING AND NUMBER. 13 

mind makes the objective the subjective. The object- 
ive means the external world, and the subjective 
means the self. And the self means one's original 
capacity to know, to feel, and to will, plus the effect 
of experiences on this power. 

4, Method is the process by which the mind of 
the learner goes from its real condition to an ideal 
condition. One's real condition is his condition just 
as he is at any time. His ideal condition is one dif- 
ferent from what he is in at any time, and which ^ 
actually has no existence except as an idea in the 
mind; hence the name ideal. The ideal condition is 
hot necessarily a better condition than the real, but 
may be either a better or worse condition. 

The Teacher's Method. — The part the teacher per- 
forms in the process of teaching is a very important 
topic of study in the subject of method. This must 
be thoroughly understood by one who is to succeed 
best. To study this is to study the teacher's method. 
And to this we turn. 

First, the teacher must think the thought in the 
point or points to be taught; that is, he must think 
the subject-matter. Secondly, he must see in terms of 
development of the learner's life the reasons for 
teaching the subject-matter; that is, he must see the 
purpose. Thirdly, the teacher must see the nearest 
related knowledge possessed by the learner which he 
can use as a foundation to build upon in teaching the 
new point; that is, he must see the basis. Fourthly, 



14 METHOD IN READING AND NUMBER. 

the teacher must see the activities the learner's mind 
pi^ts forth in mastering the points of truth in the 
subject-matter; that is, he must see the stex)s. Lastly, 
the teacher must see the means he may best employ 
in leading the mind of the learner to take the steps in 
mastering the subject-matter; that is, the teacher 
must think out the devices. Thus the teacher in 
teaching a lesson must think (1) the subject-matter; 
(2) the purpose; (3) the basis; (4) the steps; and (5) the 
devices. These five things every teacher does in 
some sort of way in teaching every lesson. Some 
think them out clearly and accurately, and some 
think them out scarcely at all, and do not know that 
they do even that much. A teacher can think the 
teaching of a single point, or of a whole lesson, or of 
a whole subject, under these five heads, and must do 
so with more or less accuracy in teaching. It is 
worth our while to study these five points further for 
the help the study will give. 

Subject-matter. — In a general way the subject- 
matter is that which is to be mastered by study. It 
is the thought embodied in the thing studied by the 
mind of the learner. In a particular lesson the sub- 
ject-matter is just that to be got from the lesson 
which the learner should have after the recitation. In 
a particular subject, as grammar or history, the sub- 
ject-matter is just that to be got from the subject 
which the learner should be in possession of after the 
study of the subject. In this general sense the sub- 



METHOD IN READING AND NUMBER. 15 

ject-matter of education is the whole world of thought. 
This study is too general to be very helpful. A closer 
study will reveal the fact that every subject-matter is 
composed of two things: 1. The facts to be taught 
or to be studied. 2. The relation in which these facts 
are to be taught or studied. 

Illustration. — Suppose the words, inquiry, dis- 
course, and aspirant are to be taught. Now, a spelling 
lesson might be made of it; and if it were a spelling 
lesson, the subject-matter would be, the words, in- 
quiry, discourse, and aspirant, as to their correct 
written or printed forms. Thus the words inquiry, 
discourse, and aspirant are the facts to be taught or 
studied, and "as to their written or printed form" 
indicates the relation in which they are to be taught 
or studied. But these same facts might be used, and 
the lesson not be a spelling lesson at all. If the rela- 
tion they are to be studied or taught in is as to their 
correct pronunciation the lesson would be one in 
orthoepy, and the subject-matter would be, the 
words, inquiry, discourse, and aspirant as to their cor- 
rect pronunciation. 

Further Illustration. — Suppose the facts of the 
revolution of the earth around the sun are taught, 
who can say whether the lesson is one in astronomy 
or one in geography? If, however, these are taught 
in their relation to the distribution of life, climate 
and relief forms on the earth's surface, the lesson at 
once reveals itself as a geography lesson. From 



16 METHOD IN READING AND NUMBER. 

these illustrations it is to be seen that a subject- 
matter consists of (1) the facts to be taught or 
studied; and (2) the relation in which these facts are 
to be considered. This relation is often called the 
organizing principle of the subject-matter. 

General Statement of Subject-matter. — The state- 
ment of a subject-matter is not the subject-matter 
any more than a word is an idea, or a sentence a 
thought. The statement of the subject-matter bears 
the same relation to the subject-matter that the word 
bears to the idea and that the sentence bears to the 
thought; that is, the statement bears the same rela- 
tion to the subject-matter that the symbol does to the 
thing symbolized. 

The general statement of a subject-matter is very 
valuable to a teacher, whether it be of a single lesson, 
or of a whole subject. It is helpful to the teacher 
because it must do two things: (1) it must name the 
facts to be taught, and (2) it must tell the relation in 
which tnese facts are to be taught. Thus the general 
statement of the subject-matter of any subject is a 
perennial guide to the teacher in teaching that sub- 
ject, in that it shows, in a general way, what to teach 
and in what relation (how) to teach it. 

Purpose. — Purpose in reality is beginning and 
ond in every process. The purpose as idea — the be- 
ginning — moves forward in the process to its realiza- 
tion — the end. The purpose exists in the teacher's 
mind» but is to be realized in the life of the learner. 



METHOD IN READING AND NUMBER. 17 

The purpose is the effe.ct the mastery of the suhject- 
matter should have on the hfe of the child. In actual 
teaching the teacher is to go from the subject-matter 
by way of comparison with the effect the thinking the 
subject-matter has on his own mind to its effect on 
the child's life, which is the purpose. That is to say, 
there is no way to tell the purpose of any subject- 
matter except from the effect its mastery produces 
on the child's life. The course of study — the subject- 
matter — is usually provided for the teacher. So the 
teacher must start with the subject-matter and find 
out the purpose in teaching it. Much depends in the 
teaching act upon how well the teacher does this. If 
the teacher has definitely in mind just what he wants 
to do in the lesson he will be drawn steadily and con- 
stantly toward its accomplishment. A definite pur- 
pose saves time, economizes energy, emphasizes the 
important, organizes, and prevents aimless wan- 
dering. 

It will be seen that I'd. teaching any lesson there 
are two phases of t*he "purpose: (1) To give knowledge 
valuable for guidance in living; (2) to give mental dis- 
cipline; that is, to furnish a mental gymnastic to the 
end that the mind may grow strong by exercising it. 

Basis. — This is the learner's nearest related 
knowledge to the new points to be taught, and upon 
which the teacher may build in teaching the new 
point. Basis is an important point in teaching. Many 
errors are made in teaching because the learner has 



18 METHOD IN READING AND NUMBER. 

not basis for learning the new point, or because the 
teacher does not see the basis. Teaching in harmony 
with the principle underlying basis, tlie mind natu- 
rally goes to the unknoionfrom the nearest related knoivn^ 
means a progressive development of a subject, each 
step becoming basis for the step succeeding it. There 
are many violations of basis in teaching, as often 
done. 

Illustration. — If the lesson to be taught is that 
5+4=9, the child must know the number 5 and the 
number 4 as basis before he could learn that 5+4 = 9. 
If the teacher should attempt to teach this lesson 
without having taught the numbers 5 and 4 he would 
meet with the difficulty of insufficient basis. Again, 
if a teacher attempts to teach the noun to a class with- 
out the class having a definite knowledge of an object, 
he will most surely meet a difficulty in the basis. The 
teacher to teach well must see and choose definitely 
his basis. 

Ste2)s. — Steps are more or less complete move- 
ments of the mind. Tliey are mental things and in 
the teaching act are in the life of the learner. They 
are the advances of the mind in mastering the sep- 
arate points of the lesson to be learned. Or in a more 
general sense they are the advances of the mind in 
mastering the various phases of a subject. 

Illustration. — If the lesson to be taught were that 
17 — 8=9, the steps would be: 1. The advance of the 
mind in rethinking the number 17. 2. The advance of 



METHOD IN READING AND NUMBER. ' 19 

the mind in rethinking the number 8. 3. The ad- 
vance of the mind in thinking the number 8 away 
from 17. 4. The advance of the mind in thinking the 
number 9 as remainder. Again, if the lesson were to 
teach the definition of the triangle, after examining 
several triangles, the steps would be: 1. The advance 
of the mind in thinking that a triangle is 'a figure. 
2. The advance of the mind in thinking a triangle 
has three sides. 3. The advance of the mind in think- 
ing a triangle has three angles. 4. The advance of 
the mind in synthesizing these points into the defini- 
tion, A triangle is a figure having three sides and three 
angles. 

To know the steps the mind takes in working out 
any new lesson is a matter of much importance to the 
teacher. He must know something of the steps or 
he can not teach at all; and, other things equal, the 
more clearly the teacher has thought the steps, the 
better will he teach the lesson. 

Devices. — The devices are the various things used 
by the teacher to lead the mind of the learner to 
think and feel in the manner desired. A synonym 
for devices is the term means. Devices, or means, 
constitute a very important factor in teaching. There 
is opportunity for the exercise of rare judgment, tact 
and skiU in the selection of devices. When it is un- 
derstood that questions, text-books, and reference 
books; maps, globes, and school apparatus in general; 
blocks, sticks, etc., are devices in teaching, some- 



20 METHOD IN READING AND NUMBER. 

thing of their importance in school work becomes evi- 
dent. Devices are so important that among many, 
method means nothing more than the manipulation of 
devices. However important they are it must not be 
lost sight of that they are always determined in the 
light of the mental process they are to induce. They 
are means to an end, and in nature the end is always 
more important than the means. 

Method as a Physical Process. — It is, perhaps, us- 
ing the term method in its most popular significance 
to think of it as meaning some physical process ex- 
ternal to the life of the learner. That is to say, it is 
using the term in the sense in which most persons 
commonly use it in speaking and writing. This idea 
of method is the one usually held by persons who 
have not made a careful study of what the term 
really ought to mean. There is a sort of indefinite- 
ness in the minds of most of such persons as to just 
what they do mean by method. However, upon ex- 
amination it will be found usually that the idea that 
method is the manner of doing some physical thing 
prevails, though even this is held in mind more or 
less vaguely. Prom thinking of method in this sense 
we have the following terms: — "Object Method," 
•'Concert Method," ''Consecutive Method," "Promis- 
cuous Method," "Catechetic Method," "Lecture 
Method," " Socratic Method," and "Laboratory 
Method." 

These all refer to the manipulation of objects, 



METHOD IN READING AND NUMBER. 21 

questions, and answers in the teaching act, and so 
are to be studied briefly under method as a physical 
process. 

The Object Method . — By this is meant the handhng 
of objects by teacher and pupils in the process of 
learning. It is a good line of work, if used judi- 
ciously. It has its proper place in teaching number 
work, primary reading, nature work, primary geog- 
raphy, and primary language. 

The Concert Method. — The concert method means 
having students to answer questions, read, and speak 
simultaneously in the recitation. There is much that 
may be said against concert work, but very httle to 
be said for it. It is objectionable because it (1) vio- 
lates the law of self activity; (2) stifles individual 
effort and individual responsibility; (3) does not bring 
out clear, definite answers or thinking; and (4) leads 
to confusion, disorder, and chaotic class work. There 
may possibly be instances in which concert work 
may be used advantageously, but as a rule it should 
be avoided. 

Tlie Consecutive Method. — The consecutive method 
of asking and answering in the recitation means be- 
ginning at some point, the head of the class, or at the 
name beginning with A, and proceeding in some regu- 
lar order back to the point of starting. In proceed- 
ing in recitation this way the students know pretty 
well when the "turn" of each one wih. come. This 
method, like the preceding one, has many things 



22 METHOD IN READING AND NUMBER. 

against it, but little to recommend it. It is objection- 
able because it leads to (1) habits of inattention; 
(2) disorder and disorganization of the class; (3) 
habits of idleness; and (4) bad methods of study. 
However good a student may be, if, when he has an- 
swered a question, he knows to a certainty that he 
will not be called upon again for some time, the tend- 
ency is for him to relax his attention. If the student 
is not a good one, the tendency in this kind of work is 
for him to become worse, and since he is not called 
upon to attend closely he is prone to do something 
else, thereby causing disorder and disorganization. 
Idleness in the class is a direct result of inattention, 
and bad habits of study result from the student's be- 
ing able to prepare just those points in the lesson 
which he has reckoned will come to him. 

Promiscuous Work. — The promiscuous method of 
asking questions and receiving answers refers to dis- 
tributing the questions and receiving answers from 
students promiscuously. No student knows to whom 
the answer to the question will fall. This method un- 
like the two preceding has much to be said for it 
and little or nothing against it. It is desirable be- 
cause (1) it fosters habits of attention and concentra- 
tion; (2) it is flexible ana gives the teacher the best 
opiX)rtunities for meeting the needs of individual stu- 
dents; (3) it fosters habits of order and organization 
in the class work; and (4) it tends to industrious 
habits, and right methods of study. By the use of 



METHOD IN READING AND NUMBER. 23 

the promiscuous method students are held constantly 
to attending to the question under consideration, to 
the careful preparation of the lesson as a whole, and 
to order and unity in the class. As a rule, the pro- 
miscuous method is certainly the best for class work. 

Catechetic Method. — This is, in its original form, 
not much used any more, and so needs very little said 
about it. According to this method the question was 
written in the text-book and just after the question 
was the answer to it. The student's business was to 
read the question, and then commit to memory the 
answer. In the recitation the teacher with text-book 
in hand read the question and the student gave, in 
the words of the text, the answer. Such a manner of 
conducting a recitation has nothing to recommend it 
and so needs no further study. 

Lecture Metliod. — The lecture method refers to 
teaching by means of talks or lectures. This method, 
perhaps, has its advantages and disadvantages. It 
is certainly not adapted to all kinds of school work, 
and probably not adapted to any kind of school work 
if used exclusively. There are, however, some phases 
of school work which may be profitably taught by 
talks, or lectures. To elementary school work the 
lecture method is not at all adapted, and but very poor- 
ly adapted to secondary school work. In the first eight 
years of the child's school life he must be taught dif- 
ferently than by this method. That stays with the 
child which he has an opportunity to see, hear, and 



24 METHOD IN READING AND NUMBER. 

think about. This, however, is not to be construed to 
mean that oral teaching should not be done in primary 
history, primary geography, nature work, etc. If the 
lecture method has any legitimate place in school 
work it is in the college and university. However 
it may seem theoretically, it remains as a fact that 
those things which are digged out by the student, 
recited upon in the class, and discussed by questions 
and answers are the things which in the end stay with 
him and do him good. Certainly the lecture method 
in the average teacher's school work is, to say the 
least, to be used sparingly, and with much caution 
when used at all. 

The Socratic Method. — This method takes its name 
from Socrates a Greek philosopher and teacher born 
469 B. C. It is sometimes called the developing 
method. It proceeds by the employment of subtle 
questions to lead the student to think what it is 
desired for him to think without telling him anything. 
"The Socratic method, more or less perfectly under- 
stood, has had great influence upon professional ped- 
agogy. In many schools for the professional training 
of teachers, and in many schools in charge of teachers 
professionally trained, systematic questioning of this 
sort is looked upon as ideal teaching ; and there is no 
lack of conscientious endeavor to prepare for use in 
recitation, series of questions which shall lead the 
child's mind to take the logical steps which given oc- 
casion requires. One who doubts the value of such 



METHOD IN READING AND NUMBER. 25 

systematic questioning may usually be converted by 
hearing a single typical recitation conducted by a 
master of the art. The power of such a recitation to 
touch, move, chasten and direct the soul is so evident, 
that if Socrates and Plato had taught us nothing but 
how to do such work their fame as teachers would be 
justified." It is noteworthy that the ''Socratic 
Method " is diametrically opposed to the "Lecture 
Method. " 

The Laboratory Method. — This is also often called 
the "Scientific Method, " and it means a procedure in 
which the student is lead to investigate and think for 
himself. It is opposed to taking things on mere 
authority without investigation, and to the text-book 
method. It proceeds by leading the student to deal 
with the actual material of study rather than to deal 
with what some one has said about it. In botany, 
studied in this way, the student deals with plants; in 
zoology, with animals; in grammar, with sentences 
and parts of sentences. This method has much to 
recommend it. 1. It fosters habits of free inquiry 
and free investigation. 2. It is the mind's natural 
way of learning. 3. It makes the student self-direct- 
ive and self -helpful. 4. It fixes with the student 
right methods of study. 5. It gives the student a 
critical attitude of mind. All these are very desirable 
characteristics for a student to have. 

Comparison of Teacher's and PupiVs Method. — These 
two methods are alike as follows : 1. They are both 



26 METHOD IN READING AND NUMBER. 

spiritual processes. 2. The mind of the learner and 
the mind of the teacher go through the same process 
in thinking the thing to be learned. 3. Both the teacher 
and the jDupil keep in mind to some extent the purpose 
of the process in the teaching act. 

These two methods are different as follows : 1. 
The teacher, in addition to thinking the truths to be 
learned, must think the learner's thinking of them. 
2. The teacher must think out the means or devices 
to be used in leading the learner to think the desired 
points of truth. 3. Wliile both the teacher and pupil 
keep in mind the purpose, the teacher sees it defi- 
nitely, or should do so, while the pupil only sees it 
vaguely. The teacher's method thus includes more 
than the learner's. 

Tivo Vieius of Method. — The foregoing study sug- 
gests to us that there are two views of method. It is 
unfortunate that educational writers hold these two 
views, as considerable confusion prevails because of 
this fact. One class of educators, those who have 
studied method least, mean by method simply the 
physical process in the act of teaching. A second 
class, those who have been special students of meth- 
od, mean by method the triple process in the act of 
teaching. 

Comparwon of tlie Two Vieivs. — In our study of 
method we may caU these two views respectively the 
popular vieiu and the special vieiv. The popular view 
wiU thus designate method as the manipulation of 



METHOD IN READING AND. NUMBER. 27 

external means, or devices, and the special view will 
designate method as the triple process. 

Thinking of method according to the popular 
view constantly places the mind's emphasis upon 
something external to the life of the learner. This 
has in the past led to much that was bad in teaching 
and is still doing so. The teacher loses sight thus of 
the fact that it is in the learner's life that the educat- 
ing process is to be carried on. He is prone to make 
the manipulating, the text-book, or some petty scheme 
of teaching an end instead of a means. Every ques- 
tion that arises concerning teaching must be settled 
in the light of the effect upon the life of the learner. 
The ultimate question is. How does it affect the life of 
the learner? The process in which the mind of the 
learner masters the new point of knowledge is the 
point of prime importance in the teaching act and the 
thing always to be emphasized in the study of the act 
of teaching. The popular view of method leads to 
almost hopeless confusion. Everyone holding this 
view who happens to use some different device, or 
means in teaching calls it his method and gives it a 
name. Since there is an almost infinite number of 
devices which may be used, there thus arises an 
almost infinite number of methods, which no teacher 
can or desires to keep informed upon. This leads to 
a hopelessly chaotic condition of things in the study 
of method. 

The popular view of method has led to much dis- 



28 METHOD IN READING AND NtJMBER. 

paragement of the study of method among persons 
who should be friendly to its study. These are often- 
times persons who are very good tliinkers, but who 
have not given special stvidy to method. It is a com- 
mon remark among this class of teachers that one 
may study method in a subject at the expense of a 
knowledge of that subject. The depreciating remarks 
made about method, which arise from the popular 
view of method, are a source of much harm to the pro- 
fession of teaching. This is true, because many 
persons who would otherwise make a careful study 
of method and would receive the benefit that must 
come to the teacher thereby, are kept from beginning 
the study by this disparaging attitude on the part of 
some teachers. It may be safely said that there is 
need for no one thing among teachers more than an 
intensely professional spirit. It seems strange that 
some teachers take pleasure in saying depreci- 
ating things about method work. It is, however, 
probably to be explained from a misconception of 
method. I have never yet heard the first person 
speak depreciatingly of method, who had been a stu- 
dent of the subject. 

The special view may be proven to be the better 
view. This is the argument : A thing is good accord- 
ingly as it realizes the purpose which brought it into 
existence. Method as a subject came into existence 
to supply the want for something, the study of which 
would help the teacher to do better work in his daily 



METHOD IN READING AND NUMBER. 29 

teaching. Accordingly, that thing whose study helps 
the -teacher most is the best. It has already been 
shown that the study of method as a triple process is 
more helpful to the teacher than the study of method 
as the manner of manipulating some external means 
or device. Therefore, the siiecial view is the better 
view of method. 

No Danger in Too Much Study. — It is not difficult 
to see that there is no danger of a teacher's devoting 
too much time to the study of method when one takes 
the proper view of method. The teacher can not 
study the process through which the mind goes in 
mastering any point of knowledge until he has the 
knowledge himself. For instance, the teacher can 
not see the mental steps the mind of the learner takes 
in learning the definition of an adjective without 
knowing the definition of an adjective himself. To 
know the method in teaching the definition of an adjec- 
tive is to know two things : 1. The definition of an 
adjective. 2. The process the mind naturally em- 
ploys in learning the definition of an adjective. No 
teacher can rationally and well teach the adjective who 
does not know these two things. 

Further Illustration. — In the teaching of history 
this point becomes quite evident. The teacher who 
knows method in history knows these two things : 1. 
The events of mankind in their relation to the strug- 
gle of the race for freedom. That is to say, he must 
know history. 2. The natural processes of the mind 



30 METHOD IN READING AND NUMBER. 

in learning history. No teacher can teach history at 
all without a knowledge of the first, and it is equally 
clear -to any person who will think, that no one can 
teach history well without a knowledge of the second. 

So this question reduces itself to the following: 
It is not possible for a teacher to study method too 
much, unless it is possible for a teacher to know too 
much about his subjects and to know too well the 
mind's natural process in learning those subjects. 

Factors Determining Method. — Nearly twenty years 
ago one of our foremost educators said, 'The law in 
the mind and the thought in the thing studied deter- 
mine the method. ' This statement can not well be 
improved upon. And it reveals the two factors which 
determine method. Tliey are (1) the law in the mind; 
(2) the thought in the thing studied. It is to be no- 
ticed that it is the law of the mind; that is, the gener- 
al truths of mental activity — the forms of acti\ity 
common to all minds. Each mind has individual 
traits, but in general, all minds act in the same way. 
The laws of mind are the forms of acti\ity common to 
aU minds. Each thing is the embodiment of thought. 
That is to say, each thing expresses thought. Long- 
fellow's "Evangeline, " the ink-stand, the maple tree 
is each the embodiment of thought. 

Illustration. — Holding in mind that method is the 
mind's process of learning, we can readily see that 
the process is different in learning things much alike. 
The activity the mind puts forth in learning the def- 



METHOD IN READING AND NUMBER. 31 

inition for the noun is very different from that put 
forth in getting the thought and f eehng from Tenny- 
son's ''Bugle Song." One cause of the difference is, 
that there is a great difference in the thought em- 
bodied in the two things. This illustrates that the 
thought in the thing studied is a factor in determining 
the method. Again, a child of six could not under 
any set of circumstances solve a difficult geometry 
problem because it would violate the laws of his mind. 
He could on the other hand learn that the printed 
word liat represents the idea hat. Thus in this case 
the law of the mind would determine the method. 

This whole study of method should emphasize the 
truth that the essential thing in teaching is opening 
up the way for the realization of the child's inherent 
possibilities. 

"Truth is within ourselves; it takes no rise 
From outward things, whate'er you may believe. 
There is an inmost center in us all, 
Where truth abides in fullness, and around. 
Wall upon wall, the gross flesh hems it in, 
****** And to know 
Rather consists in opening out a way 
Whence the imprisoned splendor may escape, 
Than in effecting entry for a light 
Supposed to be without," 



CHAPTER II. 
THE PURPOSE OF READING. 

General Meaning. — It will be remembered that 
the purpose of any subject means the effect the pur- 
suit of that subject has on the life of the learner. It 
is, of course, true that the pursuit of any subject will 
produce different effects upon different pupils de- 
pending upon the method in which the subject is 
pursued together with the individual differences of 
the students. But it remains that the purpose is to 
be determined by the effect produced in the mind of 
the learner. Thus in general we may say the pur- 
pose of reading as a school subject is the effect the 
proper pursuit of reading will produce in the life of 
the learner. 

Importance of Dejinite Idea of Purpose. — Purpose 
is both beginning and end in every process of teach- 
ing. It is beginning as an idea in the mind of the 
teacher, and it guides the process in its movement 
forward to its realization in the life of the child, the 
end. It is of first importance to the teacher to have 
clearly and definitely in mind the purpose of any 
subject before starting to teach it. And the evidence 
of this truth is that the purpose will determine : 



METHOD IN READING AND NUMBER. 33 

1. The character of the teaching process. 

2. The means used in the teaching process. 

3. The end reached by the teaching process. 
A clear, definite, fervent purpose will draw the 

teacher in teaching towards its accomplishment as 
surely as the earth draws all things toward its center. 
A clear, definite purpose saves loss of time, dissipa- 
tion of energy, and disorganized, scrappy teaching. 

Glasses of Purposes, or Aims. — For the purpose of 
helping ourselves in the study we may classify the 
aims of reading into(l) the main, or primary, aim; 
and (2) the secondary, or subordinate, aim. What is 
true of reading concerning its purpose is also true of 
any school subject. That is to say, the pursuit of 
every school subject affects the life of the learner in 
various ways, but the effects usually are divisible 
into predominant and subordinate classes. 

The Main, or Primary, Aim. — There are three 
language units, — the ivord, the sentence, and discourse. 
They had their origin as follows : The word was 
born of a desire to express an idea ; the sentence was 
born of a desire to express a thought, and discourse 
was born of a desire to express a series of coherent 
thoughts. Thus the work the word has to do is to 
symbolize an idea ; the work the sentence has to do is 
to symbolize a thought, and the work discourse has to 
do is to symbolize a series of coherent, or connected, 
thoughts. 

The subject of. reading deals with discourse as 



34 METHOD IN READING AND NUMBER. 

its language unit. Reading, of course, deals with the 
word and the sentence, too, but not as an end. It 
deals with them as a part of discourse, and as a 
means to discourse as the end. 

In teaching reading the most important thing to 
be done is to lead the learner into gaining the ability 
of getting the thought and feeling symbolized by 
pieces of printed and written discourse. And this is 
caUed interpreting discourse, or interpretation of dis- 
course. Thus the main aim of reading may be stated 
as follows : The main aim of reading as a subject is 
to give the learner skill in the intei^pretation of discourse 
in order that he may come into the possession of the 
thought and feeling of the race as embodied in history, 
literature and science. 

There are two points in this statement for the 
main purpose of reading which need special notice. 
First, reading is to give skill in interpretation. This 
means the ability to interpret readily and accurately. 
It is not sufficient that the learner can interpret dis- 
course. The world needs people who not only can do 
something, but who can do it readily and accurately, 
and this will be just the requirement in reading 
during the learner's life. So skill in interpretation 
is the thing to be aimed at — the ability to interpret 
rightly and quickly. Secondly, the experience of the 
human race is the heritage which it has left to each 
learner, and he needs to have skill in interpretation 
that he may come into his own birthright. This is 



METHOD IN READING AND NUMBER. 35 

true for this experience of the race is recorded in 
history, hterature, and science. He wants to inter- 
pret recorded history in order to come into the ex- 
perience of the race in its actual struggle for higher 
life. He wants to interpret literature in order to 
come into the experience of the race in the ideal 
struggle for higher life. He wants to interpret 
science in order that he may learn the laws of life as 
well as the great truths and forces of nature to the 
end of conforming his actions to the highest welfare 
of his own being, and to the lives of others. 

Evidence of the Main Aim. — The question. Why is 
skill in interpretation to be considered the main aim 
in reading? may be asked. The answer to this ques- 
tion is as follows : All education is to prepare the 
learner for the duties of life. The pursuit of reading 
is a part of the educational process, and should thus 
contribute its part in the process of education. The 
reading the learner will be called upon to do in life is 
predominantly silent reading ; that is, interpretation of 
discourse. It is fair to say that seventy-five per cent, 
of the reading the learner will want to do through life 
will be merely the interpretation of discourse— the 
silent reading of the daily paper, magazines, works 
of fiction, works of science, literature, catalogues, 
schedules, etc. So skill in getting the thought from 
these various kinds of discourse will be his greatest 
need which the subject of reading can supply, and 
since this is the greatest need to be supplied, the 



36 METHOD IN READING AND NUMBER. 

main aim of reading is to give skill in the interpretation 
of discourse. 

Secondary, or Subordinate, Aim. — But to give skill 
in discourse interpretation is not the only aim of 
reading. Reading as a subject comprehends the 
oral expression of the thought and feeling embodied 
in discourse, and it is the aim of the pursuit of read- 
ing as a subject to make the learner skillful in this 
also. So the subordinate aim of reading as a subject 
may be stated as follows : The subordinate aim of 
reading is to give the learner sMll in the adequate oral 
communication, in the author ^s own words, of the 
tJioiight and feeling symbolized by discourse. It is to be 
noted that the author's own words are to be em- 
ployed in the oral expression, otherwise we do not 
regard it as oral reading. If one should get well in 
mind the thought and feeling embodied in a piece of 
discourse, he might communicate this thought and 
feeling in his own language instead of the language 
of the author, but it could not be called oral reading. 
The purpose, or aim, of reading may be summed up 
as foUows: 

1^ Purpose of reading as a subject. 

1^. Main, or primary, purpose. 
1^. To give the learner skill in the interpre- 
tation of discourse in order that he may come into 
the possession of the thought and feeling of the race 
as embodied in history, literature, and science. 

2^. Secondary, or subordinate, purpose. 



Method in reading and number. 37 

1^. To give the learner skill in the adequate 
oral expression, in the author's own words, of the 
thought and feeling embodied in discourse. 

Relation of These Aims. — While these aims are 
both important in reading, the aim as to oral reading 
— the adequate communication of the thought and 
feeling in the author's own words — must be subordi- 
nated to the aim as to skill in interpretation. This is 
true for two reasons. First, it is worth much more 
to the learner in life to be able to get readily and ac- 
curately the thought and feeling from all kinds of 
discourse than to read w^eU orally. Secondly, correct 
interpretation precedes and is fundamental to cor- 
rect oral reading. It is self-evident that the learner 
can not adequately communicate the thought and 
feeling embodied in discourse when he has not come 
into possession of that thought and feeling. Skill in 
oral reading presupposes skill in interpretation. 
There is no surer way for a teacher to fail in obtain- 
ing good oral expression than by fixing his eye upon 
the oral expression to such an extent that he loses 
sight of the importance of interpretation and so 
slights it. Mistakes in oral expression usually have 
their origin in mistakes in interpretation. Some 
have even thought that if a student has the thought 
and feeling embodied in the selection, he will always 
read it well orally. But this probably puts it too 
strong, though it certainly is true that the student 
will generally read well orally, .if the interpretation 
has been well done. 



38 METHOD IN READING AND NUMBER. 

The Purposes of Reading and Literature. — The 
question for study here is, Are the purposes of read- 
ing as a subject and of hterature as a subject differ- 
ent in any way, and if different, how? A httle care- 
ful thinking on this point will show us that the pur- 
pose of reading as a subject is as different from the 
purpose of literature as a subject as the purpose of 
reading is different from the purpose of history. In 
fact they differ in very much the same way, and the 
difference is this : reading has for its purpose to give 
skill in interpretation, also in oral communication, 
while literature has for its purpose to affect the life 
of the learner by means of the thought and feeling 
embodied in the literature. In reading the learner 
reads in order that he may become skillful in read- 
ing, while in literature the uplift given by the thought 
and feeling in the selections studied is the aim. It is 
not the main aim of literature as a subject of study to 
give skiU in interpretation and in oral communica- 
tion, while in reading as a subject this should always 
be the main thing aimed at. Thus the aims of read- 
ing and literature as subjects are not at all identical. 



CHAPTER III. 

NATURE OF READING AS A SUBJECT. 

The ScJiool Curriculum. — The school curriculum 
is the school course of study. It is made up of the 
various school subjects ; as arithmetic, history, gram- 
mar, reading, spelling, geography, etc. The subjects 
in the school curriculum as a whole may be conven- 
iently divided into groups, as follows : 1. The lan- 
guage group consisting of reading, writing, spelling, 
orthoepy, etymology, lexicology, grammar, literature, 
composition, rhetoric, and primary language. 2. 
The mathematical group consisting of arithmetic, 
algebra, geometry, trigonometry, calculus and sur- 
veying. 3. The natural science group consisting of 
physiology, botany, zoology, psychology, chemistry, 
physics, astronomy, geography and geology. 4. The 
history group consisting of United States history, 
English history, and general history. 5. The art 
group consisting of drawing and music. 

The Language Group. — The language group is a 
group of subjects which have, in general, for their 
subject-matter language as a medium for communi- 
cating thought. As it was seen in previous study 
there are three language units, — the tvord, the sen- 



40 METHOD IN READING AND NUMBER. 

tence^ and discourse. Some of the subjects in the 
language group deal with the word as their language 
unit and thus are known as word studies ; one deals 
with the sentence as its language unit and thus is 
known as a sentence study; and some which deal 
with discourse as their language unit are known as 
discourse studies. The word studies are spelling, 
orthoepy, etymology and lexicology. Spelling is that 
word study which treats of the correct form of the 
written or printed word. Orthoepy is that word 
study which treats of the correct pronunciation of 
words. Etymology is that word study which treats 
of the derivation of words. Lexicology is that word 
study which treats of the meaning of words. 

The sentence study is grammar. And grammar 
may in general be defined as that language subject 
which deals with the sentence as an instrument in 
communicating thought. 

The discourse studies are reading, literature, 
rhetoric, composition and primary language. Read- 
ing, literature, and rhetoric as the science of dis- 
course, deal with discourse as a finished product, 
while composition and primary language deal with 
discourse in the process of construction — as un- 
finished. 

The following diagram will reveal the relation 
among the language subjects in the language group: 



METHOD IN READING AND NUMBER. 41 



f Spelling. 

The Word -! O^'^^oepy. 
ine vvoia , Etymology. 

t Lexicology. 

The Sentence -{ Grammar. 

r ( Reading. 

Finished - Literature. 

-r.. ( Rhetoric. 

Discourse < ^ 

I ( Composition. 

1 Unfinished -j Primary Lan- 
l ( guage. 



Language Units 



The Subject-matter of Reading. — It will be recalled 
that every subject-matter consists of two things, — 
facts and the relation in which these facts are to be 
considered. Then these two things are to be found 
in the subject-matter of reading. Now the facts to 
be dealt with in reading are facts of discourse. That 
is to say, reading as a subject deals with pieces 
of discourse. And it deals with discourse in two 
ways : ( 1 ) as to its interpretation ; ( 2 ) as to the oral 
expression of the thought and feeling which the dis- 
course symbolizes, this expression to be in the 
author's own words. By interpretation is meant get- 
ting the thought and feeling the discourse symbolizes. 
While the oral expression is important, it must not 
be lost sight of that interpretation must come first in 
importance as well as first in time. Interpretation 
is fundamental to oral expression and is presupposed 
by oral expression. There is no such thing as ade- 
quate oral expression without good interpretation. 

The following is the formal statement for the 
subject-matter of reading : The siobject- matter of read- 



42 METHOD IN READING AND NUMBER. 

ing is discourse primarily as to its interpretation and 
secondarily as to the adequate oral expression of its 
tliought and feeling in the author s own laords. 

This statement for the subject-matter of reading 
is a constant guide to the teacher who gets it well in 
mind. This is true because it tells him what to teach 
and the relation in which to teach it ; that is, hoiu, in 
general, to teach it. 

Definition of Beading. — The main thing in read- 
ing is getting the thought and feeling which dis- 
course symbolizes. This is sometimes called silent 
reading. It matters not what it is called, if teachers 
see that it is the important thing in reading, and thus, 
is the thing to be emphasized. Oral expression is 
important, but not so important as getting thought, 
because the learner wiU not use it more than one- 
tenth as much in life as he will use his ability to in- 
terpret. 

Reading is a discourse study. And it is the dis- 
course study which deals with discourse in the tw^o 
ways often indicated in these studies. The formal 
definition of reading is as follows : Beading is that 
language study ivhich deals luith discourse as to its in- 
terpretation and the oral exjwession of its thought and 
feeling in the language of the author. 

It appears from this definition that there are two 
phases of reading — interpretation and oral expres- 
si(m. These two phases are usually called silent 
reading and oral reading, and they may be defined as 



METHOD IN READING AND NUMBER. 43 

follows : Silent reading is the process of getting the 
thought and feeling embodied in discourse. Oral read- 
ing is the process of communicating aloud in the lan- 
guage of the author the thought and feeling embodied in 
discourse. 



CHAPTER IV. 
PROCEDURE IN TEACHING READING. 

Stages of Reading. — For the purpose of studying 
its method it is convenient to divide reading work 
into two stages, — the first, in a very general way, 
consisting of about the first three years of the child's 
reading work ; and the second, in a general way, con- 
sisting of the rest of the work the child does in read- 
ing in school. Various names have been given to 
these two stages. The first stage has been called the 
preparatory stage, the primary stage, the first stage, 
and the loord stage. The preparatory stage is a very 
good term, because it is significant of the fact that it 
is the stage in which the learner is preparing to do 
real reading later on. The second stage has also 
been given various names. It has been called the 
stage of reading pro2)er, the advanced stage, the second 
stage, and the discourse stage. The stage of reading 
proper is perhaps the most significant term for this. 

The Prejmratory Stage. — This stage is character- 
ized by the two following points : ( 1 ) the written or 
printed word as an isolated thing is dealt with largely 
as to the idea for which it stands; (2) the little pieces 
of discourse dealt with are not important because of 
the value of the thought they express. That is to 



METHOD IN READING AND NUMBER. 45 

say, in this stage the child will learn a vocabulary of 
written or printed words as to meaning in order that 
he may recognize them in their connection in dis- 
course later; also, he will read little pieces of dis- 
course most of which do not contain thought of per- 
manent value. Of course, some pieces he studies 
will contain thought of permanent value, but these 
will be the exceptions rather than the rule in this 
stage of reading work. 

IllMstration. — In this stage of the work the fol- 
lowing words would be good ones to teach the child : 
table, on, see, I, it, black, big, the, and a. These would 
be taught to the child so that he could recognize them 
at sight, and know both the idea for which they stand 
and their correct pronunciation. After this was done 
these words might be combined into the following 
piece of discourse and used as a reading lesson : 

I see a big hat. 

It is on the table. 

The hat is black. 

The hat on the table is black. 

The big black hat is on the table. 
In the first part of this work the child is dealing 
with words as wholes as to the ideas for which they 
stand and as to pronunciation. In the second part 
he is dealing with a piece of discourse whose thought 
is of little value. 

The Stage of Beading Proper. — This stage is 
characterized by the following: (1) discourse as a 



46 METHOD IN READING AND NUMBER. 

whole is dealt with predominantly, and the word as a 
whole is dealt with much less than in the first stage ; 
(2) discourse which embodies thought valuable in 
itself is dealt with largely. There will perhaps be 
selections dealt with whose thought is not very valu- 
able, but these will be the occasional and not the rule. 
And again, in the second stage emphasis will be upon 
the interpretation, while in the first stage oral ex- 
pression will be emphasized. 

The Starting Point. — The starting point in teach- 
ing beginning reading will be determined ( 1 ) in the 
light of what the child already knows when he comes 
to school which can be used to build upon ; that is, 
upon the basis which the average child has when he 
comes to school; (2) in the light of what the first 
reading work is. That is to say, the child must be 
led to the unknown from the nearest related known. 

Basis. — What does the average child at the age of 
six know that can be used as a basis to build upon in 
beginning to teach him reading? The answer to this 
question is, ( 1 ) he has a goodly stock of ideas of ob- 
jects, attributes, and relations in the world about 
him; (2) he knows the oral expression, or oral sym- 
bol, or oral word, for these ideas. Another way of 
saying this is, that the child has quite a good vocabu- 
lary of oral words as representing their ideas. There 
has been considerable systematic study of children's 
vocabularies with a view of finding out how many 
words the average child knows and can correctly use 



MEHTOD IN READING AND NUMBER. 47 

when he comes to school at the age of six. The fol- 
lowmg are some results of such study as reported by 
parents: "The vocabulary of Portia Bell, when two 
years old, December 1, 1899, consisted of 1,073 
words." "The vocabulary of Lyle Hugart, Valpa- 
raiso, Ind., consisted, when she was 2 years 5 months 
old, of 973 words." The vocabulary of Helen Neet, 
when 4 years 8 months old, consisted of 1,468 words. 
From these cases it seems safe to make the inference 
that the average child when he comes to school at the 
age of six has at least, a vocabulary of 1,200 oral 
words. This, of course, does not mean the child 
could define this number of words if called upon to 
do so, but it means he uses this number of words cor- 
rectly in conversation. 

The First Unknown. — Having found out what the 
child knows upon which we can build in teaching the 
first reading work, the next question is. What is the 
first unknown we want to teach the child? The thing 
the child knows is a vocabulary of oral words, and the 
first thing unknown which he must know to read the 
least bit is a vocabulary of ])rinted or written luords. 
Accordingly the starting point in teaching reading is 
to teach the child a vocabulary of written or printed 
ivords. 

Methods of Beginning. — Several methods are used 
or have been used, in teaching the child this vocabu- 
lary of written or printed words. All of the follow- 



48 METHOD IN READING AND NUMBER. 

ing are in use to a greater or less extent in various 
parts of the United States : 

1. Tlie Alphabet Method. 

2. The Synthetic Word Method. 

3. The Analytic Word Method. 

4. The Sentence Method. 

For the help we will get from the study we can 
profitably devote some time to each of these. 

The Alphabet Method. — This is no doubt the oldest 
and very poorest method of teaching beginning 
reading. The Greeks in ancient Athens used this 
method 2,500 years ago. According to this method 
the teacher proceeds to teach the children the alpha- 
bet by rote. The teacher points to a letter and pro- 
nounces its name and asks the child to pronounce it; 
then he points to another, pronounces it, and asks the 
child to pronounce it ; then another, and another, and 
so on through the alphabet. This sort of thing is 
kept up from day to day until the child knows the 
names of the letters at sight, successively, promis- 
cuously, or in an inverse order. 

The next general movement is to teach the chil- 
dren to spell orally small words made up, of course, 
of the letters whose names the children know. This 
line of work may be begun before the children have 
learned the names of all the characters of the alpha- 
bet. Thus these two lines of work — (1) learning the 
names of the letters by rote ; and (2) learning to spell 
orally — overlap. 



METHOD IN READING AND NUMBER. 49 

After having learned to spell, and pronounce 
orally a number of words in the manner indicated 
above, the children are started to read small pieces 
of discourse made up of the words they have been 
learning to spell orally. When they come to new 
words, according to this method, the children are 
encouraged to spell them out. 

It is evident that this method must be a very slow 
and difficult way for the children to learn to read. 
In fact, from a pedagogical view point, it has not one 
feature to recommend it. There are numerous things 
to be said against it, but nothing to be said for it. 
The following are the objections to it : 

1. It is, for a long time, the most formal and 
driest sort of rote work. 

2. It is almost wholly .devoid of inherent interest 
to the children. 

3. The children have no basis for the work. 

4. It ignores the children's knowledge of words, 
which constitutes the real basis for beginning read- 
ing work. 

5. It gives children a dislike for school work. 

6. It encounters the difficulties which arise 
from the dissimilarity between the names of letters 
and their sounds when combined into words and 
syllables. 

7. The practice of having children to spell out 
the new words leads to halting, hesitating habits of 
reading. 



50 METHOD IN READING AND NUMBER. 

One would scarcely think that this method is 
used extensively at the present stage of educational 
progress in the United States, but it is still used in 
many places. 

The Synthetic Word Method. — The term si/nthetic 
means a putting together. So from the significance 
of the term, the inference one would make is that 
something is put together to make up the word. And 
this is right, for words are built up of the sounds 
composing them, according to this method. Thus the 
oral word is built up, but since the child is well 
acquainted with the oral word, he readily associates 
it with the printed or written word. 

This method with slight variations has been 
given all the following names : Synthetic Word 
Method; Phonic Method : Phonetic Method: and Pollard 
Method. 

By this method the teacher proceeds to teach the 
child the sounds which the various letters of the 
alphabet symbolize. Since the vowels and some of 
the consonants symbolize more than one sound, the 
diacritical marks must be used with the letters. The 
names of the letters are not learned at first, but some 
fanciful name is given, and the child and the teacher 
"play" that it says so and so — the sound which the 
letter symbolizes. Thus fi is called an old man, and 
the teacher and children "play " that he says ae ; fi is 
called the little lamb, and the teacher and children 
"play" that it says u, fi, fi; :i is called the little old 



METHOD IN READING AND NUMBER. 51 

woman and they "play" that she says ah, ah, ah; b 
is called the baby and they "play " that it says the b 
sound ; p is called a steamboat ; f is called a cat ; v is 
called a bug ; d is called a dove ; z is called a bumble 
bee ; g is called a frog ; r is called a dog ; th is called 
a goose ; ch is called a locomotive, etc. All the sym- 
bols of the various sounds are thus given "play 
names," and the children learn the sound symbolized 
by each symbol in play. 

After the sounds of the symbols have been well 
learned in this way, the teacher says to the children, 
"Now we have just been playing that this (a) is an 
old man. Would you like to know its real name?" 
The children will want very much to know, and will 
say so. The reason that they will want to know is 
this : naturally, as soon as the child knows the mean- 
ing of anything, he wants to know its name. The 
children in this case know the sounds the letters 
symbolize, which is the meaning of letters and the 
only meaning, and so naturally want to know their 
right names. The teacher then tells them the right 
name of the symbol, and thereafter calls it by the 
right name when speaking of it with the children. 
The children are also encouraged to call it by the 
right name when they speak of it. Thus they learn 
the name without any special effort ; that is, incident- 
ally. 

The method of learning the names of the other 
letters of the alphabet is as nearly like that in learn- 
ing the name of a as possible. 



52 METHOD IN READING AND NUMBER. 

Having now taught the sounds the various char- 
acters symbolize, and the names of the various char- 
acters of the alphabet, the teacher next leads the chil- 
dren to recognize written or printed words at sight 
as the symbol of oral ivords. The procedure is as fol- 
lows : The teacher writes or prints the sentence, 
ihe hat i§ on the b6x, or any other simple sentence 
on the board, and asks the children to tell vvhat the 
words are. Each word is worked out first, then the 
whole "story" is asked for. If any trouble arises in 
working out the words, the teacher calls for the 
sound of each symbol separately, but it is better to 
get the whole oral word, if possible. For instance, if 
the child could not pronounce the at sight, the teacher 
would ask for the sound of th, then the sound of e, 
then for the whole word. This makes it very easy 
for the child, since he well knows what sounds the 
various symbols represent. 

After reading this one sentence, the teacher puts 
a second on the board using several of the old words 
but some new ones. Then another sentence, and 
another; then simple pieces of discourse containing 
mainly old words, but always introducing some new 
ones. 

Then pieces of discourse gradually increasing in 
complexity are used, and soon the book is put into 
the hands of the pupils, and they move rapidly for- 
ward. 

Merits and Demerits.— The Synthetic Word Method 



METHOD IN READING AND NUMBER. 53 

of teaching beginning reading has both its merits and 
its demerits. The following may be considered as 
points in its favor : 

1. It takes advantage of the play instinct in 
children, and is thus very interesting for them. 

2. It takes advantage of the basis consisting of 
a vocabulary of oral words which the children have. 

3. It tends to make the children self -helpful in 
working out the pronunciation of new words. 

4. It tends to habits of clear, distinct enuncia- 
tion, and correct pronunciation. 

5. It makes the teaching of diacritical marks 
easy. 

The following may be noticed as objections to it : 

1. It is unnatural for the child to build up 
words ; he naturally learns them as wholes first. 

2. It leads the child to make the association be- 
tween the oral word and the printed or written word, 
while he should make the association between the 
printed or written word and the idea which it sym- 
bolizes. 

3. He starts to read discourse in which the dia- 
critical marks are used, which is not the kind he will 
be called upon to read throughout his life. 

4. Trouble is experienced in changing from one 
to the other. 

There are some other objections to this method, 
but these are the chief ones. 

It should be said that many good teachers use 



54 METHOD IN READING AND NUMBER. 

this method in teaching beginning reading, and have 
remarkable success. Others succeed better by some 
other method. 

A few years since the Synthetic Word Method 
was very popular in many sections of the country, 
but recently it has been losing in popularity and 
favor. 

The Sentence Method. — By this method the child is 
taught whole sentences as symbolizing thoughts. 
Thus the child is in some way stimulated to think and 
to indicate to the teacher what thought he has ; the 
teacher then puts on the board the sentence which 
symbolizes the thought and endeavors to lead the 
child to associate the thought and this symbol. The 
following will indicate the procedure : 

The teacher asks the child with what he plays, 
and he says "I play with a ball." The teacher then 
says "I shall put on the board what makes me think 
what you said," and writes or prints on the board "I 
play with a ball." The teacher then asks the child 
what the sentence says. A second question is then 
asked; it may be, "What is the color of your ball?" 
The child answers "My ball is red." The teacher 
again says "I shall put on the board what makes me 
think what you said," and writes or prints "My ball 
is red. " Then, as before, the teacher asks the child 
what the sentence says. If the child should not start 
readily, the teacher continues with sentences con- 
taining the same or very nearly the same words till 



METHOD IN READING AND NUMBER. 55 

he thus becomes famihar with a f ew sentences, there- 
after varying the sentences. 

This method of teaching beginning reading is put 
tolerably plainly by saying the teacher engages the 
child in some interesting conversation, and uses his 
sentences as material for the reading work. 

After a time the sentences with which the child 
is familiar are broken up into their parts — the words. 

There are some advantages claimed for the sen- 
tence method as well as some objections urged 
against it. 

The following are claimed as advantages : 

1. It gives a tendency to the mind to grasp sen- 
tences as wholes in reading. 

.2. From this grows the ability to interpret 
readily, and to communicate easily in reading. 

This may all be said by saying it tends to make 
light readers. Some persons in reading interpret 
the selection word by word and are, for that reason, 
called heavy readers. Others grasp whole sentences, 
and some even whole paragraphs, in one act of the 
mind in interpreting discourse and are, for this 
reason, called light readers. That is to say, some 
use many times as much energy in reading as others 
use. It is claimed, and it seems with some degree of 
vahdity, that the sentence method tends to make 
light readers. 

The following are some objections to the sentence 
method : 



56 METHOD IN READING AND NUMBER. 

1. It leads the child to make an indirect associa- 
tion between the symbol, the sentence, and the 
thought, while the association should be direct. This 
appears from the fact that the teacher gets the child 
to use the oral sentence, and tells him she is going to 
place on the board what he says, or something to that 
effect, the child making the association between the 
oral sentence and the written or printed sentence 
instead of between the written or printed sentence 
and the thought. 

2. The sentence which the child learns as a 
whole is not what he will find used as he learned it 
very often in his life. But if he should learn a word 
as a whole, he would very frequently find it in after 
life just as he learned it. 

3. The sentence method furnishes poor oppor- 
tunities for making the association between the sym- 
bol and the idea or thought symbolized strong. But 
if this association is not made strong the child can 
not remember what the words and sentences are; 
that is, he will not recognize them at sight, which is 
the thing aimed at. 

The Analytic Word Method. — The word method of 
teaching primary reading is usually understood to 
mean what some have called the "Analytic Word 
Method, " and w^hat will be discussed in detail here 
under the title of Analytic Word Method. According 
to this method written or printed words are taught 
as wholes as symbolizing their ideas, or as to their 



Method in reading and number. 57 

meaning. After a number of words have been taught 
as wholes these same written or printed words are 
analyzed into the parts which symbolize the parts of 
the oral word — the sounds. 

Definite Procedure. — The first thing to be done in 
teaching by the Analytic Word Method is to teach the 
children a vocabulary of written or printed words as 
standing for their ideas. Various teachers teach with 
good success a vocabulary of from 40 to 75 words in 
this first work. The following is the way it is done : 

Let the lesson be to teach the children the printed 
or written word, nest, as a symbol of the idea, nest. 
The teacher presents an actual nest to the children 
and tells them to hold up their hands, if they know 
what it is; then a second one is presented, and a 
third, and thus several. The teacher then puts the 
word on the board calling the attention of the chil- 
dren to it by saying "I am going to make a word on 
the blackboard which makes me think what I have in 
my hand. " The teacher holds a nest in her hand in 
the meantime. The children thus make the associa- 
tion between the word and the idea it symbolizes. 
The steps in the above process are as follows : 

1. The advance of the learner's mind in re- 
thinking the old idea. 

2. The advance of the learner's mind in adjust- 
ing itself to the symbol — the word. 

3. The advance of the learner's mind in making 
the association between the idea and the symbol. 



58 METHOD IN READING AND NUMBER. 

Each of these steps should be studied briefly. In 
the first the learner rethinks the old idea; that is, 
thinks it again. It is old to him, because he learned 
what a nest is sometime in his life before he came to 
school. The object of having the actual nest before 
him is to get him to rethink the old idea. Several 
nests are presented in order that the idea may be 
general, that is, apply to any nest, instead of just one 
particular nest, which might result from presenting 
but one nest. 

In the second step the child looks at the symbol, 
gives his attention to it, and this is what is meant by 
adjusting his mind to it. In this, as in the first step, 
the word should be in several places on the board, 
and it should be found in other places ; as on a chart, 
in the book, on cards, etc., in order that the symbol 
may be understood to be general. It is a good plan 
to have it written in various sizes in different colored 
chalk. 

While aU three of these steps are important, the 
last is the one upon which depends the value of all 
three. It is very desirable that the learner recognize 
the word at sight ever after the lesson. He will do 
this surely if the association is made strong enough. 
Otherwise he is likely to forget the word before the 
next lesson. So special pains must be taken to have 
the association strongly made. It may be done as 
follows : 

1. Have the children point out with a pointer the 



MEHTOD in reading ANt) NUMBER. 59 

words on the board which say what the teacher has, 
the teacher handhng the object. 2. Have the child 
bring the object when the teacher points to the sym- 
bol. 3. The child finds the word on cards, on charts, 
and in books. 

It is to be noted in this work that the oral word 
is not used until the very close of the lesson, then 
some child is called upon to tell what the word is; 
that is, pronounce the oral word. The purpose of 
keeping the oral word in the background is, that the 
child may get into the habit of making the association 
directly between the written or printed symbol and 
the idea, and not indirectly between the written or 
printed symbol and the oral word, and from the oral 
word to the idea. Thus if when the child sees the 
word, nest^ the idea comes first into the mind, it is 
because those things have been directly associated. 
But if, when he sees the word, nest, the oral word 
comes first into mind and then the idea, it is because 
the association between the written or printed symbol 
and the idea has been made indirectly. Two evils are 
said to grow out of making the association between 
the written or printed word and the oral word, and 
then between the oral word and the idea. They are 
as follows : 

1. It tends to make heavy, slow, hesitating read- 
ers. It wastes energy. 

2. It tends to give children the habit of using 
the vocal organs — working the hps, etc. — in silent 



60 METHOD IN READING AND NUMBER. 

reading:. Both of these habits are undesirable, the 
second being very annoying in school work. 

Adjectives and Action Words. — The teaching of the 
word, nest, is a fair example of how all nouns are to be 
taught in this first work in reading. Adjectives and 
action words are not quite so easily taught, yet they 
are to be taught in substantially the same way. That 
is to say, the following three steps are taken : 1. Tlie 
child is led to rethink the old idea. 2. He is led to 
adjust his mind to the symbol — the written or printed 
word. 3. He is induced to make the association 
strong between the idea and its symbol. 

Tlie, A, An, Is, Can, On, In, etc. — Such words as 
these are the ones which are the most difficult to 
teach in this first work in reading. The point of diffi- 
culty is in getting the learner to rethink the old idea. 
The following will indicate what is probably the best 
way to proceed with these words. Assume that the 
child knows the words, hat, and black, tliey having 
been taught to him before as indicated above. The 
teacher asks the child to tell her the color of the hat, 
and the cliild responds ''TJie hat is black. ^^ The 
teacher says "I shall place on the board the words 
which make me think what you said, " and writes the 
sentence on the board. Some child is then asked to 
point out h(tt and black. The children are then asked 
to tell the new words. In most cases they will get 
the new words at once. If they do not do so readily, 
the teacher asks some child to tell the story again 



METHOD IN READING AND NUMBER. 61 

while the others watch. Then some child is asked to 
tell what the first word, "T/^e," says, then the next, 
and the next, and the next. This is kept up until the 
children have well in mind the and is. Then this sen- 
tence, The black hat is on the box, may be obtained 
from the children by placing the black hat there, and 
By placing some differently colored hat on a chair. 
The teacher places the sentence on the board and thus 
teaches the word, on, in the same general way as the 
and is were taught. 

It will be noticed that this way of teaching is a 
combination of the word method and the sentence 
method. 

Fixing the Vocabulary in Mind. — One of the most 
important points in teaching the child a vocabulary 
of written and printed wt)rds is fixing each word well 
in the learner's mind as he proceeds. Unless this is 
done the rest of the work is pretty much of a failure. 
There are two good ways to do this, as follows: 1. A 
hst of the words should be kept in some convenient 
place oii the board and reviewed from day to day. In 
this review the teacher may ask for a word and have 
some child point it out with a pointer, or the teacher 
may point to the word and ask some one to pronounce 
it. The former way is better. 2. The second way 
to fix the vocabulary in the child's mind is to combine 
the words he learns into small pieces of discourse, 
and give him driU in reading them. 

Both these ways are based upon the principle, 



62 METHOD IN READING AND NUMBER. 

two or inort' tJiuigs he/d together in consciousness the mofit 
often, other things equal, are the tnost strongly associated. 
Print and Script. — The question, Shall we begin 
with print or script? always comes up for considera- 
tion in method in reading. Perhaps the most satis- 
factory answer to this question is, that it makes little 
or no difference which is taught first. Many good 
and successful teachers prefer to begin with the 
script, but the same may be said with respect to the 
print. There are points of advantage in either way. 
The following seem to favor beginning with print: 

1. The most of the learner's reading in life will 
be reading of print, and so this is the most important 
for him to learn. 

2. If the learner first learns script he must soon 
change from it to print, which will of necessity be 
attended with some waste of energy. 

Beginning with script seems to have the follow- 
ing in its favor : 

1. It makes busy work more easy to conduct. 

2. It tends to make children equally good read- 
ers of script and print. And this is true of very few 
persons. 

Personally I prefer to begin with print for the 
first dozen or so lessons, then introduce the script 
and carry the two along side by side. 

Beading of Simple Pieces of Discourse. — As soon as 
enough written or printed words have been well 
learned, small pieces of discourse should be formed 



METHOD IN READING AND NUMBER. 63 

from them. These pieces are used for reading 
lessons for the children. And a little later the learner 
begins reading from the chart or first reader. The 
interpretation of these pieces of discourse is easy, 
and the thought embodied is usually of no permanent 
value, but the oral expression is very important. The 
child here begins to form his habits of oral expres- 
sion, and whether he ever becomes a good reader or 
not depends largely upon these habits. However 
much trouble it may be, the learner must not be per- 
mitted to form habits of halting, hesitating, monoto- 
nous oral expression. This is a critical period in the 
teaching of primary reading. 

Analysis Work. — It will be remembered that we 
are studying what is called the Analytic Word Method 
of teaching primary reading. But up to the present 
no analytic work has been studied. This is not, how- 
ever, because no analytic work should be done in the 
actual work in reading up to this place, but because 
in our study we must take the points consecutively, 
and we have just now reached the topic. Analytic Work. 

This analysis, w^hich is to be carried along with 
much emphasis through the entire preparatory stage 
of reading, consists in separating the oral words cor- 
responding to the written and printed words which 
the child has been studying, into their parts, the 
sounds, and the association of these sounds with their 
symbols ; that is, with the corresponding parts of the 
written and printed word. 



64 METHOD IN READING AND NUMBER. 

The following will show the nature of this work : 
The child has learned the printed and written word, 
boj; as a symbol for an idea, in the way already shown. 
The teacher writes the word on the board and has 
some child to pronounce it, thus getting the oral word 
before the class. The children are then led to see 
the tirst sound in the oral word and to make it; then 
the second, and the third ; next, they are led to see 
that b symbolizes the tirst sound ; o, the second, and 
X, the third. The steps the child's mind takes with 
these words are as follows : 

1. The advance of the learner's mind in rethink- 
ing the oral word. 

2. The advance of the learner's mind in analyz- 
ing the oral word into its sounds. 

3. The advance of the learner's mind in analyz- 
ing the written word into the parts corresponding to 
the sounds. 

4. The advance of the mind in making the asso- 
ciation between the sounds and their symbols. 

These steps are very general. A close analysis 
would break up each one into several smaller steps. 
But these are the general steps in the analysis of any 
word. 

First Step. — The way to lead the children to take 
the first step is to write the word on the board, and 
ask the class how many know it, then call on some 
one to pronounce it. The test of his rethinking is 
his pronouncing it. 



METHOD IN READING AND NUMBER. 65 

Second Step. — The analysis of the oral word into 
its sounds is a step of some difficulty with the first 
few words, but offers little trouble thereafter. Per- 
haps the best way to proceed at first is for the teacher 
to analyze the oral word into its sounds and have the 
children watch and give the analysis from imitation. 
This will be necessary with only a few words, for the 
children will soon gain much ability in this work. 
Soon they will be able to give original analyses. 

Third Step and Fourth. — The third and fourth 
steps may best be taken together. Thus the child is 
led to see that certain parts of the symbol symbolize 
the different sounds in the oral word. He infers that 
h in the word hox symbolizes the first sound in the 
oral word; o, the second, and x, the third. The 
teacher tells him this is right and thus gives him a 
start. Practice soon gives him considerable skill in 
this work. 

Time of Doing the Analytic Work. — This analytic 
work may well be begun almost from the first ; that 
is, as soon as the child has learned a dozen or so 
words as symbols of their ideas ; and it should be 
carried on through the entire first stage of reading 
with considerable emphasis, at the least. It will 
probably be found necessary to do some of it at vari- 
ous places through the second stage of reading. 

Purpose of Analysis. — This work is an extremely 
important kind of work in teaching reading, and a 
kind of work that is not generally well enough done. 



66 METHOD IN READING AND NUMBER. 

It is important because it has the following purposes: 

1. It makes the child self-helpful in the pronun- 
ciation of new words. 

2. It enables him, to a large extent, to work out 
the new words as to pronunciation as he comes to 
them in reading. 

3. It helps the child in forming the habit of dis- 
tinct enunciation, and correct pronunciation in oral 
reading and in speaking. 

4. It tends to enable the child to acquire these 
habits from the relation of the symbols of the sounds, 
and not by use of the diacritical marks or the dic- 
tionary. 

Working Out Neiu Words as to Pronunciation. — In 
taking up the new lessons for study in the first stage 
of reading and the first year or two of the second 
stage words new as to pronunciation will be met with 
by the children, and the best way to deal with these 
words has been a problem to many teachers. It is 
safe to lay down the law that in dealing with these 
words the ivork must he of such a character as to lead tlie 
students to do the luork for themselves and to make them 
self-ltelpful in such work. Work of the following 
character will certainly do this : In general, it may 
be said that the learner is to be led to work out the 
new words by seeing parts of old ones whose pronun- 
ciation he knows, in the new ones. For instance, ago, 
things, called, loved, and blue-bell are the new words in 
a lesson. The children have already had the words. 



METHOD IN READING AND NUMBER. 67 

a, go, think, running, call, played, love, sad, blue and 
bell. So if the children can be led to put together a 
and go; tli, ing and s; call and ed; love and d; blue 
and bell they will have the pronunciation of the new 
words. The child will not do this without lessons 
leading him into the habit of doing so. In pursuit of 
this idea the teacher may make some such assign- 
ment as this to the children: "Study your lesson 
through carefully and make a list of aU the new words 
and all the old ones you can not pronounce. See how 
many you can work out the pronunciation of by hunt- 
ing for old words or parts of old words in them. 
Make a hst of words which you think wiU help in pro- 
nouncing the words you can not pronounce." It is 
evident that this kind of assignment tends to lead the 
children into the habit of working out the pronuncia- 
tion of words for themselves — the thing desired. If 
the children do not have the pronunciation of the 
words worked out, and they would not ordinarily have 
all worked out, the teacher places one of the words 
on the board, and asks if any one can see anything 
old in it. If the children do not, the teacher writes 
some old word on the board which wiU give them a 
start and so on until the word is worked out ; then the 
next word, and the next till aU the words have been 
pronounced by the children. 

The new words the children meet will be of these 
two kinds: (1) those that can be pronounced by 
analogy, such as things, called, etc; (2) those that 



68 METHOD IN READING AND NUMBER. 

can not be taught by analogy, such as through, ivomen, 
etc. This second class may be taught in the same 
way as the, is, can, a, and an were taught. 

Diacritical Marks. — These are characters which 
indicate the sounds the various letters symbolize when 
used in words. They are the macron (-), the breve 
(-), the caret ( ^ ), the dieresis ( •• ), the semi-dieresis 
(.), the tilde (^), the cedilla (.), and the suspended 
bar (-^). 

The diacritical marks and their uses should be 
taught to children in their reading work. And the 
purpose of this work is to enable, the child to use the 
dictionary intelligently and with facility. And this 
is the whole purjiose of teaching diacritical marks. 

If the analysis of words has been carried along 
through the first stage of reading, the teaching of dia- 
critical marks becomes an easy task. This work 
should begin as early as the second year, and should 
be continued until the work is loell learned. 

Second Stage. — In the first stage of reading the 
beginning of correct habits of oral expression was a 
very important part of the work, and the pieces of 
discourse dealt with were in the main not important 
because of the value of the thought symbolized. In 
the second phase of reading the emphasis is placed 
upon the interpretation of the discourse, that is, get- 
ting the thought and feeling the discourse symbol- 
izes; and the discourse dealt with in the main is 



METHOt) IN READING AND NUMBER. 69 

important because of the value of the thought and 
feehng it symboHzes. 

Didactic and Symbolic Discourse. — In this phase of 
reading both didactic and symbolic discourse will be 
dealt with, and thus they come up for study here. 

Didactic discourse is also called scientific dis- 
course, perhaps because it is the kind employed in all 
scientific treatises. It directly sets forth truth. For 
instance, if one should say that man is irritable, fero- 
cious, and bloodthirsty, the characteristics of the 
man are set forth directly and the sentence is an ex- 
ample of didactic, or scientific, discourse. But if one 
should say that man is a tiger, the characteristics of 
the man are set forth indirectly, and the sentence is 
an example of symbolic discourse. The tiger is the 
symbol, or type. 

Symbolic discourse is also called literary dis- 
course, perhaps because what is known as literature 
is largely symbolic discourse. It sets forth truth 
indirectly by means of a symbol, or type. The fol- 
lowing will illustrate the two kinds : The young of 
dragon-flies are found in ponds and streams about 
which the adults fly, and are most abundant among 
the stems of submerged plants ; they are also found 
crawling over the bottoms of ponds and streams 
where there are no plants growing. They vary 
greatly in form, some being slender while others are 
very broad. They live and grow this way till a day 
comes when an inner impulse causes them to climb 



70 METHOD IN READING AND NUMBER. 

some weed stem; their backs split open and the adult 
dragon-iiies come out, dry their wings and fly away. 
The above is purely didactic. Why V 

The following is literary or symbolic: 

"To-day I saw the draofon-fly 

Come from the wells where he did lie. 

An inner impulse rent the veil 

Of his old husk ; from head to tail 

Came out clear plates of sapphire mail. 

He dried his wings : like gauze they grew : 

Through crofts and j^astures wet with dew 

A living flash of light he flew." 

"Excelsior," "Evangeline," "The Chambered Nauti- 
lus," "To a Waterfowl," "The Great Stone Face," 
and "Sour Grapes " are other examples of symbolic 
discourse. 

Steps in Symbolic Discourse. — In mastering a piece 
of symbolic discourse as a reading lesson evidently 
the first thing the learner meets with is the language, 
whose mastery is the first step. The language re- 
veals the symbol, the mastery of which is the second 
step. The symbol reveals the leading thought, or 
theme, whose mastery is the third step. A fourth 
step is the mastery of the adaptation of the symbol to 
the leading thought. And the last step is the oral 
reading of the selection. Thus every reading lesson 
which deals with symbolic discourse is like every 
other one in that the mind takes the following steps 
in mastering it: 



METHOD IN REAt)ING AND NUMBER. ?! 

1. The mastery of the language. 

2. The mastery of the symbol, or picture. 

3. The mastery of the leading thought. 

4. The mastery of the adaptation of the symbol 
to the leading thought. 

5. The adequate oral expression of the thought 
and feeling in the author's words. 

The language is to be mastered in two ways : 
first, as to the meaning of the separate words in their 
connection ; and, secondly, as to the pronunciation of 
the different words. 

By the mastery of the symbol, or picture, is 
meant that all parts of the story as presented by the 
language are to be learned and vividly held in mind. 
There are several terms here used as synonyms to 
mean the same as the symbol. The terms symbol, 
picture, type, embodiment, and conception are all 
more or less in use. This second step is an import- 
ant one in teaching reading. Many teachers do not 
lead their children by their assignments to master the 
symbol and thus fail to some extent in teaching read- 
ing. 

Every selection which is organized and is worth 
spending one's time upon as a reading lesson has 
some leading thought around which all the subordi- 
nate thoughts cluster. This leading thought is the 
most important thing in the selection. It is the mes- 
sage the selection bears to humanity, and the under- 
standing of it is the key to the correct interpretation 



7^ METHOD IN READING AND NUMBER. 

of the selection. Therefore, in teaching reading, the 
mastery of the leading thought, or theme, is a very- 
important step. 

By the adaptation of the symbol to the leading 
thought is meant that the various parts of the picture 
are chosen because they are good to suggest the 
theme and make it strong. That is to say, the parts 
of the picture and the picture as a whole are adapted 
to set forth the thought. For instance, if one says a 
man is a donkey, he means that the donkey, the sym- 
bol, is well adapted to set forth the stubbornness of 
the man, the leading thought. The mastery of the 
adaptation of the symbol to the theme is of prime im- 
portance in teaching reading. In leading the learner 
to master this step opportunities for rare skill and 
tact in teaching present themselves. 

After the four steps discussed above have been 
taken the learner should have well in mind the 
thought and feeling of the selection, and should thus 
be in a good condition to read well the selection orally. 
And this remains to be done as the last step. 

Steps in Didactic Discourse. — The steps in master- 
ing a jMece of didactic discourse are not the same as 
in mastering a piece of symbolic discourse. Didactic 
discourse has no symbol, or embodiment; and since 
this is true, steps two and four in the symbolic dis- 
course are absent in the mastery of didactic dis- 
course. Then the mind in mastering selections of di- 
dactic discourse takes the fohowing steps: 



METHOD IN READING AND NUMBER. 73 

1. The mastery of the language. 

2. The mastery of the leading thought, or theme. 

3. The adequate oral communication of the 
thought and feeling in the author's words. 

Summary. — The following will summarize the 
steps in teaching reading, granting that the analytic 
loord method is the method employed: 
I. First Stage. 

1^ The mastery of a vocabulary of words 
as symbolizing their ideas. 

1^. Steps with each word. 

1^. The advance of the learner's 
mind in rethinking the old idea. 

2^. The advance of the learner's 
mind in adjusting it to the written or printed symbol. 
3^. The advance of the learner's 
mind in associating the symbol and the idea. 

2\ The interpretation and oral reading 
of small pieces of discourse made up from the words 
which the child has in his vocabulary. 
3 ^ A line of analysis work. 
1^. Steps with each word. 

1^. The advance of the learner's 
mind in rethinking the oral word. 

2^. The advance of the learner's 
mind in analyzing the oral word into its sounds. 

3^. The advance of the learner's 
mind in analyzing the written word into the symbols 
of the sounds. 



/4 METHOD IN READING AND NUMBER. 

4•^ The advance of the learner's 
mmd m associating the sounds with their symbols. 

4^ A line of teaching the diacritical 
marks. 

II. Second Stage. 

1^ The mastery of symbolic discourse. 
12. Steps. 

1^. The mastery of the language. 
2^. The mastery of the symbol, or 
picture. 

3^. The mastery of the central 
thought, or theme. 

4^. The mastery of the adaptation 
of the symbol to the leading thought. 

5^. The adequate oral communica- 
tion of the thought and feeling the discourse em- 
bodies in the author's own words. 

2^. The mastery of didactic discourse. 
12. Steps. 

1^. The mastery of the language. 
2^. The mastery of the leading 
thought. 

3"^ The adequate oral communica- 
tion. 



Chapter v. 

CONCRETE ILLUSTRATIONS. 

Advantages of. — A good teacher should always be 
able to make clear his points with good concrete il- 
lustrations, and one who does not do so will find his 
teaching lacking much in effectiveness. Concrete il- 
lustrations make the thoughts stand out in clear relief 
and bring the desired truths before the mind so viv- 
idly that they are easily retained and reproduced. 
Therefore, for the help that comes from the study we 
will consider in this chapter some concrete illustra- 
tions. 

EXCELSIOR. 
The shades of night were falling fast, 
As through an Alpine village passed 
A youth, who bore, mid snow and ice, 
A banner with the strange device, 
Excelsior! 

His brow was sad; his eye beneath 
Flashed like a falchion from the sheath, 
And like a silver clarion rung 
The accents of that unknown tongue, 
Excelsior! 

In happy homes he saw the light 

Of household fires gleam warm and bright; 

Above, the spectral glaciers shone, 



METHOD IN READING AND NUMBER. 

And from his lips escaped a o;roan, 
Excelsior! 

"Try not the Pass!" the old man said; 
" Dark lowers the tempest overhead, 
The roaring torrent is deep and wide!" 
And loud that clarion voice replied, 
Excelsior! 

"Oh stay," the maiden said, "and rest 
Thy weary head upon this breast!" 
A tear stood in his bright blue eye, 
But still he answered with a sigh. 
Excelsior! 

" Beware the pine-tree's withered branch! 
Bew^are the awful avalanche!" 
This was the peasant's last Good-night, 
A voice replied, far up the height. 
Excelsior! 

At break of day, as heavenward 
The pious monks of Saint Bernard 
Uttered the oft-repeated prayer, 
A voice cried through the startled air, 
Excelsior! 

A traveler, by the faithful hound. 
Half-buried in the snow was found, 
Still grasping in his hand of ice 
That banner with the strange device, 
Excelsior! 

There in the twilight cold and gray, 
Lifeless, but beautiful he lay. 
And from the sky, serene and far, 
A voice fell, like a falling star. 
Excelsior: 



METHOD IN READING AND NUMBER. 77 

The mind, if left to pursue its own course in mas- 
tering this selection of symbolic discourse as a read- 
ing lesson, (1) will read the selection through to get a 
general idea of it as a whole; (2) will study it 
through in detail taking the five steps indicated above 
in the mastery of a selection of symbolic discourse. 

In the mastery of the language the meaning of 
the words, Aljnne, Excelsior, falchion, clarion, spectral, 
glaciers, loiuers, avalanche, monks, Saint Bernard, etc., 
will be mastered; also, the words passed. Excelsior, 
Alpine, beneath, falchion, glaciers, pass, lowers, blue, 
etc., will be mastered as to their pronunciation. 

In the mastery of the picture, or symbol, the 
youth with his various attributes, the mountains, the 
Alpine village, the banner, the happy homes, the 
glaciers, the old man, the tempest, the roaring tor- 
rent, the maiden, the pine-tree's withered branch, 
the avalanche, the peasant, the monks of Saint Ber- 
nard, etc., will be got well in mind in their proper 
relation. 

In the mastery of the theme the real meaning of 
this whole picture will be worked out. The picture 
itself has meaning, but the deeper meaning beyond 
itself and to which it points is the theme. Longfellow 
is not simply telling about a rash young man who lost 
his life in climbing the Alps mountains. The selec- 
tion bears a message to humanity and the picture 
symbolizes this message. And getting this well in 
mind is what is meant by mastering the theme. 



78 METHOD IN READING AND NUMBER. 

In the mastery of the adaptation of the picture to 
the theme the reason for choosing a youth, for start- 
ing him at dusk, for having him to cHmb a mountain, 
and for having him to lose his hfe will be shown. 
Also, the significance of the banner, the village, the 
maiden, the old man, the pass, the glacier, the tor- 
rent, the awful avalanche, the peasant, the monks, 
the falling voice, etc., will be shown as contributing 
to the leading thought. 

The oral reading of the selection comes as the 
last step, and should not offer much difficulty after 
the other four steps have been well done. 

The following is an assignment which has for its 
purpose to lead the learner in working through Ex- 
celsior as a reading lesson : 

1. Read the selection through very carefully 
and try to see what it means. 

2. Master the meaning and pronunciation of any 
unfamiliar words in the selection. 

3. Get in mind well the details of the picture 
presented in this poem. 

4. What is the leading thought in the selection ? 
Give good reasons for your opinions. 

5. Wliy is a youth chosen? 

6. Enumerate the characteristics of the youth 
and tell why each one is given. 

7. What is the significance of the happy homes, 
and of the maiden ? 

8. Wliat is the significance of the lowering tem- 



METHOD IN READING AND NUMBER. 79 

pest, roaring torrents, spectral glaciers, pine-tree's 
withered branch, and the awful avalanche? 

9. Why must the youth lose his life? 

10. What is the meaning of the voice that fell, 
like a falling star ? 



80 METHOD IN READING AND NUMBER. 

ERASTUS WREN'S VIRTUE. 

Erastus Wren was virtuous, in spirit and in letter. 
Was very virtuous and good, and daily growing better; 
And so immaculate was he, his neighbors, men and maids, 
They daily looked to see the wings sprout from his shoulder 
blades. 

He wouldn't eat rice; he wouldn't drink tea no more than he'd 
drink rum. 

For they were grown by heathen hands in darkest heathen- 
dom; 

He'd have no fellowship, he said, with men who thus behaved, 

Nor boom the industries of men so totally depraved. 

So he lived devoid of coffee and of cocoanuts and spice, 
And when his folks had lemon pie he never touched a slice; 
And he'd never taste of pudding; nay, unless, beyond a doubt. 
The cook deposed and guaranteed all nutmeg was left out. 

He wouldn't wear cotton shirts at all, because he was afraid 
The girls who work in cotton mills are sometimes underpaid; 
And once he thought he'd wear no wool, it gave him such a 

shock 
When he was told that one black sheep was found in every 

flock. 

And he never read the papers, and he never would begin, 
He said they reeked with wickedness, iniquity and sin; 
He wouldn't consult the dictionary, nor turn a leaf, not he. 
Because he said it held bad words no good man ought to see. 

There was no food for him to eat, no clothes for him to wear, 
No mental sustenance at all to suit him anywhere; 
And so he died, — the thing to do to round out his perfection, — 
And not a living man arose to make the least objection. 



METHOD IN READING AND NUMBER. 81 

Assignment. — The following assignment should 
lead the learner in mastering the above selection as a 
reading lesson: 

1. Read the poem through carefully as a whole. 

2. Master any unfamiliar words found in it both 
as to meaning and as to pronunciation, 

3. Get carefully in mind all the characteristics 
of Erastus Wren. 

4. What in your judgment is the message the 
poem has for humanity? Give reasons for your 
opinion. 

5. Try to show the adaptation of any part of 
the embodiment to the theme. 

6. Read the lesson orally so as to bring out the 
thought and feeling as you understand it. 



82 METHOD IN READING AND NUMBER. 

THE GOLDEN TOUCH. 

King Midas loved money very much, but not 
quite as well as he loved his little child, Mary. He 
thought yellow gold was the most beautiful thing he 
had ever seen, and he wanted to get as much of it as 
he could. Yet King Midas was a very rich man. He 
had boxes of this yellow money, and every day he 
looked at it for a long time. 

Once when he was looking at his gold, and think- 
ing how beautiful it was, he saw a man standing by 
his side. "You are very rich. King Midas," said the 
man. "Well, yes; I have some money," said the 
King. "Do you care for more?" said the man. "Oh, 
yes," said King Midas "I have only a very little, after 
all. " Well, " said the man, "I shall be glad to help 
you. You may make any wish you like, and I will 
grant it to you." King Midas thought a long time 
about this wish. What could he wish that would give 
him all the gold he wanted ? At last he had a happy 
thought. He would wish that everything he should 
touch might turn to gold ! Then he told the man his 
wish. How he laughed to hear that this rich old king 
still wanted so much more money! "At sunrise to- 
morrow morning," said the man, "your wish shall be 
granted. Then everything you touch shall turn to 
gold. I will give you the Golden Touch. " 

The old king slept very little that night. As soon 
as the sun rose in the morning, he put his hand on 
his bed. His wish had been granted. There was his 



METHOD IN READING AND NUMBER. 83 

bed turning into yellow gold. Wlien he put on his 
clothes, they, too, were gold. He took up a book on 
the table, and its cover became yellow, and he saw it 
had golden leaves. He went around the room and 
touched everything. Each turned to gold, and he 
thought his room was very beautiful. 

The King was very happy when he called little 
Mary to come and sit down and eat. As soon as the 
King touched his cup, it was gold. When he took a 
bite of fish, it, too, turned into gold, and he could not 
eat it. Then he tried to eat his egg and bread, but 
he could not. They were hard, yellow gold. Poor 
King Midas was very hungry! Everything was so 
beautiful, he was so rich, and yet he could not eat a 
bite! "What is the matter, father? Why don't you 
eat?" said little Mary. And she came and stood by 
his side. The king kissed her and said, "My dear 
little girl, go and eat your bread and milk." But 
what was the matter ? The sweet, rosy face was now 
yellow, and the soft, pretty curls were hard. The 
little girl he had loved so well, King Midas had turned 
into gold. " What have I done?" cried the poor king. 
"My dear little child ! My Mary!" 

Just then he saw the same man standing at his 
side who had given him the Golden Touch. "Well, 
King Midas, how do you like the Golden Touch?" said 
the man. "I am so unhappy!" said the King, still 
looking at his little daughter. "Unhappy!" said the 
man. "Did I not do as I satid I would? Do you wish 



84 METHOD IN READING AND NUMBER. 

more gold still?" "Oh, no, no!" said Midas. "I 
have lost what I loved more than gold, — my little 
child, Mary! Give her back to me alive and well!" 
"Ah," said the man, which is the better, the gift of 
the Golden Touch or a cup of cold water?" "The 
cup of water, " said Midas. "And which is the bet- 
ter, the Golden Touch or your own little Mary as she 
used to be?" "My child, my dear child!" cried the 
king. " I would not give one of her little soft curls 
for all the gold you might give me !" "Tell me. King 
Midas, said the man, "shall I take away the Golden 
Touch?" "Oh, yes, indeed !" said the king. "You 
are a better man than you were yesterday. King Mi- 
das, and I will take away the gift of the Golden 
Touch, if you wish. Go to the brook just back of the 
garden and wash, and bring a cup of the same water 
back with you. " 

The King lost no time in going to the brook. He 
jumped into the water, saying, " I do hope this wiU 
wash away the Golden Touch. Why did I ever want 
it, I should like to know." He filled the cup, and 
walked back to the house very fast. The first thing 
he did was to put water on his little Mary. Then the 
old rosy color came back, she laughed, and was his 
own loving child again. Then he went about the 
house and made everything as it was before he had 
turned it into gold. The old King never wished again 
for the Golden Touch. 



METHOD IN READING AND NUMBER. 85 

The above lesson from the Indiana Second Read- 
er is a piece of symbolic discourse, though it is not 
poetry. The steps in teaching it are the same in 
general as in teaching any other piece of symbolic 
discourse, namely: 

1. The advance of the learner's mind in getting 
a general idea of the lesson as a whole. 

2. The advance of the learner 's mind in master- 
ing the language. 

3. The advance of the learner's mind in master- 
ing the details of the picture or symbol. 

4. The advance of the learner's mind in seeing 
and feeling the central thought. 

5. The advance of the learner's mind in master- 
ing the adaptation of the picture to the central 
thought. 

6. The adequate oral communication of the 
thought and feeling. 

With children of the second or third grade these 
steps would have to be worked out slowly, many 
questions being given by the teacher in assignments 
on each point. Let us assume that we have a second 
grade class, and study the following assignment: 

1. Read the whole lesson through and tell me 
what you learned about it. 

2. Make a list of all new words and any old ones 
whose meaning or pronunciation you do not know. 
Make a list of old words which you think will help you 
in working out the pronunciation of those you do not 
know. 



86 METHOD IN READING AND NUMBElt. 

3. How many persons are spoken of? What are 
their names? Tell all that is said about each one. 

4. Do you believe this story? Why? Does it 
tell us anything true? Wliat? 

5. Why does this story have a king in it? Why 
gold? Why a man who could give the king the 
Golden Touch? Why a little girl ? 

6. Read it orally so as to bring out the meaning 
as you understand it. 



METHOD IN READING AND NUMBER. 87 

ORCHARD LIFE. 

"An orchard is an excellent place for Nature 
Study. Here live many kinds of tiny creatures, ep^ch 
kind with its own peculiar mode of life. Some have 
comparatively simple life histories, merely eating 
and growing and finally laying eggs for another gen- 
eration; but others undergo wonderful transforma- 
tions, and still others exhibit an instinct that seems 
much like reason. And even those that appear to 
live the most humdrum existence are well worthy of 
careful study, for their lives are never as simple as 
they seem at first sight. 

By a study of orchard life there may be learned 
also much that is of immediate practical importance; 
some of the most dreaded insect pests infest fruit 
trees. A thorough knowledge of the ways of these 
depredators enables us to plan successfully methods 
of destroying them, and thus to prevent their 
ravages." 

In the mastery of the above lesson there are in 
general but three steps to be taken, for this lesson is 
purely didactic, or scientific. 

It is no doubt true that reading books should be 
made up largely of literary, or symbolic discourse, 
and some have gone so far as to say that no other 
kind of discourse properly has a place in text-books 
on reading. But if it be true that the selections the 
child reads in school are to be of the kinds he wiH 



88 METHOD IN READING AND NUMBER. 

read throughout his Ufe, in order to tit him for all 
kinds of reading, a reading book must contain selec- 
tions of both symbolic and didactic discourse. 

There is also a place in teaching reading for what 
is called sight reading; that is, the reading of selec- 
tions orally without having studied them beforehand. 
A goodly quantity of this kind of work should be done 
in the most successful teaching of reading. 



ABOU BEN ADHEM. 

Abou Ben Adhem — may his tribe increase ! 
Awoke one night from a deep dream of peace, 
And saw within the moonlight in his room, 
Making it rich and like a lily in bloom. 
An angel writing in a book of gold. 

Exceeding peace had made Ben Adhem bold; 

And to the presence in the room he said, 

"What writest thou?" The vision raised its head. 

And, with a look made of all sweet accord. 

Answered, "The names of those who love the Lord." 

"And is mine one?" said Abou. "Nay, not so," 
Replied the angel. Abou spoke more low. 
But cheerly still; and said, "I i)ray thee, then. 
Write me as one that loves his fellow-men." 

The angol wrote, and vanished. The next night 

It came again, with a great wakening light, 

And showed the names whom love of God had blessed; 

And, lo ! Ben Adhem's name led all the rest. 



CHAPTER VI. 

COMMON ERRORS IN TEACHING READING. 

Opportunities for. — While reading has been in our 
school curriculum as long as any subject, and is as 
generally taught as any school subject, it is by no 
means an easy subject to teach well. The opportuni- 
ties for errors are many, and because of this reading 
is generally taught much more poorly than it should 
be. The following may be mentioned as the most 
common of these errors : 

1. The use of the alphabet method in teaching 
beginning reading. 

2. A lack of sufficient phonetic work. 

3. Too much emphasis on oral reading to the 
exclusion of interpretation. 

4. A lack of sufficient thought interpretation. 

5. Indefinite, general assignments. 

Each of these wiU be studied briefly for the help 
that comes of the study. 

The Use of the Alphabet Method. — It seems that at 
the present stage of educational progress it should be 
needless to call attention to the fact that to begin to 
teach reading by having the children to learn the 
names of the letters of the alphabet by rote is unped- 
agogical in the extreme, and so, exceedingly bad 



90 METHOD IN READING AND NUMBER. 

teaching. There are, however, many teachers still 
teaching in this way, and many persons who believe 
in it, and also many who do not even know there is a 
more natural, more interesting and better way. The 
objections to the alphabet method have been stated 
before, and though they should be rethought, they 
will not be repeated here. 

Phonetic Work, or Sound Analysis. — A lack of suf- 
ficient work in analyzing oral words into sounds, and 
associating these sounds with their symbols is the 
cause of several bad results in teaching reading. 1. 
It leaves children helpless in the pronunciation of 
new words. 2. It leaves with children bad habits of 
enunciation. 3. It makes their language in speaking 
and reading hard to understand. 4. It makes the 
teaching of diacritical marks much more difficult. It 
is certainly a great mistake not to carry on in the 
child's reading work aline of systematic phonic work. 

Oral Reading to the Exclusion of Interpretation. — It 
is often customary in teaching reading to cover a 
rather large amount of discourse by having the chil- 
dren go through with it by pronouncing the words. 
This is called oral reading even when the learner does 
not get the thought himself, to say nothing of com- 
municating it to some one else. This is a mistake 
because it gives the learner the wrong notion of the 
nature of reading as weU as bad habits of reading. 
It is not the large quantity of discourse gone through 
which is the criterion of success in reading. It is the 



METHOD IN READING AND NUMBER. 91 

power of ready, accurate interpretation plus the abil- 
ity of adequate oral communication in the author's 
words which constitutes the criterion of success in 
teaching" reading. And this may come from dealing 
with comparatively few pieces of discourse rightly 
taught, while it will certainly not come from dealing 
with a multitude of selections wrongly taught. 

Lack of Thought Interpretation. — It will be re- 
called that the larger part of reading is what is called 
silent reading, or interpretation of the thought, and 
that the other part is the oral communication of this 
thought and its accompanying feeling. Now, no one 
can communicate thought which he does not have. 
Then interpretation, or thought getting, is funda- 
mental to communication, or oral reading. As simple 
as this problem is, it certainly is the besetting sin in 
teaching reading that teachers ask their pupils to 
read orally — to communicate thought and feeling — 
when they have it not to communicate. A lack of 
thorough interpretation on the part of the student 
before an attempt is made to read orally is at the root 
of nearly all the errors that occur in oral reading, also. 
There are at any rate two very bad things that result 
because of not sufficient emphasis on interpretation 
in teaching reading. 

1. The learner never becomes sufficiently skill- 
ful in getting the thought and feeling from discourse. 

2. The extremely small number of students who 
really become good oral readers. 



9^ METHOD IN READING AND JSfUMBEll. 

Indefinite, General Assignments. — An indefinite, 
general assignment is a very bad error on the part of 
the teacher in teaching any subject. But this truth 
applies with unusual force to teachers of reading as 
the work is usually done. Most of us can remember 
our own experience as students in reading, and it 
comes forcibly to our own minds that our lessons in 
reading were assigned by the teacher's saying "Take 
the next lesson. " We can also remember that we did 
not know how to take it, when to take it, nor where to 
take it. And most of us were surely not much better 
off by the taking. With such an assignment as indi- 
cated above, the child will usually read over the les- 
son, which often does not take more than ten or fifteen 
minutes, and think he has it prepared for recitation. 
It is almost the universal experience of teachers of 
reading that they do not succeed in getting the stu- 
dents to study their reading lessons sufficiently. 
The main cause of this trouble lies with the teacher, 
and is to be found in the poor assignments given. If 
the teacher will see to it that every assignment in 
reading presents definite problems to be mastered, 
and conscientiously holds the children to the mastery 
of these problems, the difficulty in getting them to 
study their reading lessons sufficiently will largely 
disappear. 

There is no other means in the hands of the 
teacher that may be used so effectively in making his 
teaching of reading a success as his assignments. 



CHAPTER VII. 

SUPPLEMENTARY READING. 

Nature of. — In connection with the material in the 
text-book in reading other things should be placed in 
the hands of the children to read. Much of this kind 
of material should be used in what is called sight 
reading; that is, reading by the children without 
their having made previous preparation on the selec- 
tion. Now, this kind of work is known as supple- 
mentary reading, and the selections are caUed mate- 
rial for supplementary reading. 

Need and Value of. — There is much need for sup- 
plementary work in teaching reading. This need is 
for the following reasons, which may be put as pur- 
poses of supplementary reading : 

1. To put more life and interest in the reading 
work, and thus make it easier for both the pupils and 
the teacher. 

2. To make the students more quick in inter- 
pretation and oral expression. 

3. To lead the pupils to love good literature, and 
thus into the habit of reading good literature. 

A Difficulty .— AR teachers recognize the value of 
supplementary reading and the desirability of having 
such work, yet many do not have the material and do 
not know where to get it. 



94 METHOD IN READING AND NUMBER. 

To help teachers in obtaining such material a list 
of books and selections suitable for each grade is 
here arranged. These lists will be of books not only- 
approved by our own judgment, but by the judgment 
of educators the country over. It is not expected 
that any teacher will be able to secure all these books, 
but some of them will doubtless be available for al- 
most any earnest teacher. 

FIRST YEAR. 

1. Classic Stories for Little Ones, McMurry, Public 

School Publishing Co., Bloomington, 111. - - .40 

2. Twilight Stories, Foulke, Silver, Burdett and Co., 

Chicago. .35 

3. Cyr's Primer, Ginn and Co., Chicago. - - - .30 

4. The Werner Primer, The Werner School Book Co., 

Chicago. - - 

5. Our Little Book for Little Folk, American Book Co., 

Chicago. - - .40 

6. Cyr's First Reader, Ginn and Co., Chicago. - - .35 

7. Fables and Rhymes for Beginners, Ginn and Co., 

Chicago. .30 

8. Hodskin's Little People's Reader, Ginn and Co., Chi- 

cago. .30 

9. Baldwin's First Reader, American Book Co., Chi- 

cago. ------ -- - .25 

10. Stories for Kindergartens and Primary Schools, 

Wiltse, Ginn and Co., Chicago. - - - - .35 

SECOND YEAR. 

1. Robinson Crusoe for Boys and Girls, McMurry, 

Public School Publishing Co., Bloomington, 111. - .25 

2. Grimm's Fairy Tales, Wiltse, Ginn and Co., Chicago. .35 



METHOD IN READING AND NUMBER. 95 

3. Stories Mother Nature Told Her Children, Ginn and 

Co., Chicago. -------- .50 

4. Easy Steps for Little Feet, American Book Co., Chi- 

cago. _---._-- - - .25 

5. Verse and Prose for Beginners, Houghton, Mifflin 

and Co., Chicago. .25 

6. First Year Nature Reader, Werner School Book Co., 

Chicago. - 

7. The Riverside Reader and Primer, Houghton, Mifflin 

and Co., Chicago, 205 pages. . . - - .30 

8. Johonnot's Book of Cats and Dogs, American Book 

Co., Chicago. .17 

9. The Hiawatha Primer, 147 pages, Houghton, Mifflin 

and Co., Chicago. ------- .40 

10. Cooke's Nature Myths, A. Flanagan, Chicago. - 

THIRD YEAR. 

1. Scudder's Fables and Folk Stories, 200 pages, Hough- 

ton, Mifflin and Co., Chicago. - - . - .40 

2. Stories of Indian Children, Public School Publishing 

Co., Bloomington, 111. - - - - . - .50 

3. Cyr's Third Reader, Ginn and Co., Chicago. - .45 

4. Stickney's ^sop's Fables, Ginn and Co., Chicago. .40 

5. Short Stories of our Shy Neighbors, American Book 

Co., Chicago. -------- .50 

6. Golden Book of Choice Reading, American Book 

Co., Chicago. - - - - .... .30 

7. Book of Tales, American Book Co., Chicago. - .50 

8. Peabody's Old Greek Folk Stories, Houghton, Mifflin 

and Co., Chicago. ....... .25 

9. Myths of Old Greece, Pratt, Ginn and Co., Chicago. .60 
10. Heart of Oak No. II. D, C. Heath and Co., Chicago. 

FOURTH YEAR. 
1. Hawthorne's Wonder Book, Houghton, Mifflin and 

Co., Chicago. - - - .40 



96 METHOD IN READING AND NUMBER. 

2. Hawthorne's Tanglewood Tales, Houghton, Mifflin 

and Co., Chicago. ---..-. .40 

3. Kingsley's Water Babies, Ginn and Co., Chicago. .45 

4. Francillon's Gods and Heroes, Ginn and Co., Chi- 

cago. . - . - .50 

5. Baldwin's Old Stories of the East, American Book 

Co., Chicago. - - - .45 

6. Stories from Arabian Knights, Houghton, Mifflin 

and Co., Chicago. .40 

7. Ruskin's King of the Golden River, etc., Houghton, 

Mifflin and Co., Chicago. - - -" - - .25 

8. Black Beauty, A. Flanagan, Chicago. - - 

9. Pioneer History Stories, McMurry, Public School 

Publishing Co., Bloomington, 111. - - - .50 

10. Stories of Great Americans, American Book Co., 

Chicago. - - .40 

FIFTH YEAR. 

1. Anderson's Fairy Tales, Second Series, Ginn and 

Co., Chicago. - - - .45 

2. Bunyan's Pilgrim's Progress, by Montgomery, Ginn 

and Co., Chicago. .35 

3. Stories of Our Country, American Book Co., Chi- 

cago. - . . - . .40 

4. Lays of Ancient Rome, Houghton, Mifflin and Co., 

Chicago. .25 

5. The Voyage to Lilliput and Brobdingnag, Houghton, 

Mifflin and Co., Chicago. - . - - - .40 

6. Hawthorne's Wonder Book, Houghton, Mifflin and 

Co., Chicago. .40 

7. Polly Oliver's Problem, Houghton, Mifflin and Co., 

Chicago. - - .60 

8. The Children's Life of Lincoln, McClurg and Co., 

Chicago. 1-25 



METHOD IN READING AND NUMBER. 97 

9. First Book in American History, Eggleston, Ameri- 
can Book Co., Chicago. - - - - - .60 
10. Heroes of Asgard, MacMillan Co., Chicago. - .50 

SIXTH YEAR. 

1. Frye's Brooks and Brook Basins, Ginn and Co., 

Chicago. - - - - .70 

2. Ten Boys on the Road from Long Ago to Now, Ginn 

and Co., Chicago. -60 

3. Burrough's Birds and Bees, Houghton, Mifflin and 

Co., Chicago. -60 

4. Franklin's Autobiography, by Montgomery, Ginn 

and Co., Chicago. ------- .50 

5. Longfellow's Evangeline, Houghton, Mifflin and Co., 

Chicago. - - '25 

6. Irving' s Sketch. Book. 

7. Arabian Knights, by Hale, Ginn and Co., Chicago. .55 

8. Hughes' Tom Brown at Rugby, Ginn and Co., Chi- 

cago. - - - - - .60 

9. Lamb's Talks of Shakespeare, Houghton, Mifflin 

and Co., Chicago. ------- .50 

10. Scudder's George Washington, Houghton, Mifflin 

and Co., Chicago. - - - .40 

SEVENTH YEAR. 

1. Scott's Lady of the Lake, Ginn and Co., Chicago. .45 

2. Swift's Gulliver's Travels, Ginn and Co., Chicago. .40 

3. Dana's Two Years Before the Mast, Houghton, Mif- 

flin and Co., Chicago. -60 

4. Hawthorne's Tales of White Hills, Houghton, Mifflin 

and Co., Chicago. -40 

5. Washington's Rules of Conduct, Diary, Letters, and 

Addresses, Houghton, Mifflin and Co., Chicago. - .25 

6. Wiltse's Jean Valjean, Ginn and Co., Chicago. - 1.05 
1. Wiggin's The Story of Patsy, Houghton, Mifflin and 

Co., Chicago. (Fine) -60 



98 METHOD IN READING AND NUMBER. 

8. Ball's Star-Land, Ginn and Co., Chicago. - - 1.10 

9. Wyss' Swiss Family Robinson, Ginn and Co., Chi- 

cago. .55 

10. Hawthorne's Biographical Stories, Houghton, Mifflin 

and Co.. Chicago. .25 

EIGHTH YEAR. 

1. Low^ell's Vision of Sir Launfal, and Other Poems, 

Houghton, Mifflin and Co., Chicago. - - - .25 

2. Two Great Retreats of History, Ginn and Co., Chi- 

cago. .60 

3. Scott's Talisman, Ginn and Co., Chicago. - - .60 

4. Lamb's Adventures of Ulyses, Ginn and Co., Chi- 

cago. - -- .35 

5. Starr's American Indians. 

6. Plutarch's Lives, Ginn and Co., Chicago. - - .55 

7. Coffin's Story of Liberty, Chas. Scribner's Sons, New 

York. 1.00 

8. Long's Ways of Wood Folk, Ginn and Co., Chi- 

cago. - -- -..-.'. .60 

9. Stories from English History, by Blaisdell, Ginn 

and Co., Chicago. ------- .50 

10. Hawthorne's House of Seven Gables, Houghton, Mif- 
flin and Co., Chicago. .70 

In the preparation of these lists of books and 
selections, the name of the publisher and the price of 
the book have been given in most instances. A few 
which were unknown to the writer have been omitted. 
In these cases your book dealer in your own town 
will be able to order the book for you without any 
additional cost. 



.OH 



CHAPTER VIII. 

NATURE AND ORIGIN OF NUMBER. 

Nature of Number. — We shall assume in our stud- 
ies in method in number that number is a mental, or 
spiritual, thing and try hereafter to be consistent 
with this assumption. In making this assumption in 
our studies four views of what number is must be 
considered for the purpose of clearness. These views 
are as follows : 

1. There are those who hold that number is an 
inherent property of objects. 

2. There is a view that number is the relation 
between magnitudes, or quantity. 

3. There is a view that number is the mind's 
idea of the times one magnitude is applied in measur- 
ing another. 

4. And lastly, some are to be found who hold 
that the symbol of the mind's idea of the times one 
magnitude is applied to another in measuring it is 
number. This view makes the figures the numbers. 

Illustration. — Thus 5 apples by the first view is 
regarded as meaning one, one, one, one, and one 
separate particular apples, the thing which makes 
each a one being the unity, or particularity, inherent 
in the object. Number in this sense is qualitative, 
for it is qualities which makes each object a one. 

L.olC. 



100 METHOD IN READING AND NUMBER. 

5 apples according to the second view means that 
the whole quantity of apples is measured by the 
quantity, one apple, and that the relation between 
these two magnitudes, is the number. 

According to the third view the mind's idea of 
the relation between these two magnitudes, one apple 
and five apples, is the number. 

The fourth view is that the figure 5 is the num- 
ber. 

The following from McLellan and Dewey's Psy- 
chology of Number is suggestive on these points : 

"Number is not a property of the objects which 
can be realized through the mere use of the senses, or 
impressed upon the mind by so-called external ener- 
gies or attributes. Objects aid the mind in its work 
of constructing numerical ideas, but the objects are 
not number. Nor does the bare perception of them 
constitute number. A child or an adult may perceive 
a collection of balls or cubes, or dots on paper, or a 
bunch of bananas, or a pile of silver coins, without an 
idea of their number; there may be clear and ade- 
quate percepts of things quite unaccompanied by 
definite numerical concepts. No such concepts, no 
clearly defined numerical ideas, can enter into con- 
sciousness till the mind orders the objects — that is, 
compares and relates them in a certain way. " 

The above based upon the genesis of number in 
the mind is argument against the first view of num- 
ber presented above. 



Method in reading and number. lOl 

Genesis of Number, — By genesis -of number is 
meant the mental process in which number ideas 
arise. That is to say, the mind performs certain 
activities in getting number, and these processes 
constitute the genesis of number. 

This process is as follows : 1. The mind grasps 
a magnitude as a vague whole. 2. The mind brings 
into consciousness a smaller magnitude of the same 
kind. 3. The mind measures the larger magnitude 
by the smaller. 4. The mind grasps the times the 
smaller magnitude was applied to the larger in the 
process of measurement; that is, the mind grasps 
the number. 

Illustration. — Suppose the number is 8 ft. The 
meaning is, that a larger magnitude 8 ft. as a whole 
has been grasped ; then the smaller magnitude 1 ft. 
has come into consciousness, and that this has been 
applied eight times in the measure of the larger 
magnitude. 

Or suppose the number is 5 boys. The meaning 
is, that the larger magnitude 5 boys as a whole has 
been grasped ; then the smaller magnitude 1 boy has 
come into consciousness, and this magnitude has 
been applied five times in measuring the larger 
magnitude. 

The following helps on this point: "The idea 
of number is not impressed upon the mind by objects 
even when these are presented under the most favor- 
able circumstances. Number is a product of the 



102 METHOD IN READING AND NUMBER. 

way in which the mind deals with objects in the oper- 
ation of making a vague whole definite. This opera- 
tion involves (a) dlscrimmaUon or the recognition of 
the objects as distinct individuals (units ); (b) gener- 
alization, this latter activity involving two subproc- 
esses; (1) abstraction, the neglecting of all charac- 
teristic qualities save just enough to limit each object 
as one] and (2) grouping, the gathering together the 
like objects (units) into a whole or class, the sum.^^ 

And from the nature of number presented in the 
above analysis the author draws the following con- 
clusions concerning the teaching of number : 

1. "Number can not be taught by the mere pre- 
sentation of things, but only by such presentation as 
will stimulate and aid the mental movement of dis- 
criminating, abstracting, and grouping which leads 
to definite numerical ideas." 

2. "It is clear that to promote the natural action 
of the mind in constructing number, the starting 
point should be not a single thing or an unmeasured 
whole, but a group of things or a measured whole. 
Attention fixed upon a single unmeasured object will 
discriminate and unify the qualities which make the 
thing a qualitative whole, but can not discriminate 
and relate the parts which make the thing a definite 
quantitative whole." 

Definition of Number. — Prom the above study we 
get the definition of number considered from the 
viewpoint of the psychology of number. This defini- 



METHOD IN READING AND NUMBER. 103 

tion is as follows : Number is the mind's idea of the 
times one magnitude is applied in measuring another. 
This seems the most helpful definition of number 
whether one looks at it from the viewpoint of the 
genesis of number or from the viewpoint of the way 
the mind uses its number ideas in the practical affairs 
of life. It is, to say the least, the best working defi- 
nition for one in the study of the method of teaching 
number. 

Origin of Number. — In the study of the nature 
and genesis of number the mind's natural mode of 
forming number ideas was seen. But the question 
for study here is, What is the reason the mind per- 
forms these activities? The mind does not do this 
without a necessity for it, and this reason, this neces- 
sity we want to discover. The study of limitation 
gives us help on this problem. 

Limitation. — "If every human being could use at 
his pleasure all the land he wanted, it is probable that 
no one would ever measure land with mathematical 
exactness. There might be, of course — Crusoe-like 
— a crude estimate of the quantity required for a 
given purpose; but there would be no definite 
numerical valuation in acres, rods, yards, feet. 
There would be no need for such accuracy. If food 
could be had without trouble or care, and in suffi- 
ciency for every-body, we should never put our ber- 
ries in quart measures, count off eggs and oranges by 
the dozen, and weigh out flour by the pound. If 



l04 METHOD IN READING AND NUMBEli. 

every-thing that ministers to human wants could be 
had by every-body just when wanted, we should never 
have to concern ourselves about quantity. If every- 
thing with which human activity is in any way con- 
cerned were unlimited, there would of course be no 
need to inquire respecting anything whatever : What 
are its limits? How much is thereof it? Even if a 
thing were not actually unlimited, if there were al- 
ways enough of it to be had with little or no expendi- 
ture of energy, it would be praGtically unlimited, and 
hence would never be measured. It is because we 
have to put forth effort, because we have to take 
trouble to get things, that they are limited for us, 
and that it becomes worth while to determine their 
limits, to find out the quantity of anything with which 
human energy has to do." 

Limitation is the fundamental idea in all magni- 
tude. If there were no limitations upon things there 
would be no necessity for measuring magnitudes, 
and hence no necessity for number. 

This same principle may be worked out in 
another way by considering the relation between 
means and end. "If all our aims were reached at the 
moment of forming them, without any delay, post- 
ponement, or countervening occurrences — if to re- 
alize an end we had only to conceive it — the necessity 
for measurement would not exist, and there would be 
no such thing as number in the strictly mathematical 
sense." But the end to be realized is often remote 



METHOD IN READING AND NUMBER. 105 

and complex so that to realize it distance in space, re- 
moteness in time, and various hindering circumstan- 
ces must be overcome. In adopting the proper 
means, quantity, or magnitude, of some kind must be 
considered, and thus measurement. And from this 
the necessity of number arises. 

"The conscious adjusting of means to end, par- 
ticularly such an adjusting as requires comparison of 
different means to pick out the fittest, is the source of 
all quantitative ideas — ideas such as more and less, 
nearer and farther, heavier and hghter, etc. Quan- 
tity means the valuation of a thing with reference to 
some end; what is its worth, its effectiveness, compared 
with other possible means. These two conceptions — 
(a) the origin of quantitative ideas in the process of 
valuation (measuring) and (b) the dependence of val- 
uation upon the adjusting of means to an end are the 
beginning of all conceptions of quantity and number, 
and the sound basis of dealing with them." 

"Number arises in the process of the exact 
measurement of a given quantity with a view to insti- 
tuting a balance, the need of this balance, or accurate 
adjustment of means to end, being some limitation." 

Thus we have reached the following conclusions 
from our study of the origin of number : 

1. There is a limitation upon all things man de- 
sires. 

2. There is the necessity of adapting means to 
end in man's life. 



106 METHOD IN READING AND NUMBER. 

3. Out of these conditions there is the necessity 
for measurement. 

4. The necessity in the mind for exact ideas of 
measurement is the origin of number. 

Note. — The quotations in this chapter are from The 
Psychology of Number by McLellan and Dewey. 



CHAPTER IX. 
METHOD OF PROCEDURE IN TEACHING NUMBER. 

Points to Be Kept in Mind. — In studying the pro- 
cedure in method in number, there are some points 
in the theory studied before, to be kept constantly in 
mind because of the guidance they furnish. Some of 
these points are as foUows : 

1. Limitations transform things into quantity, 
giving them a certain undefined magnitude as size, 
buDr, weight, time, etc. 

2. This vague whole of quantity is changed into 
definite ideas of quantity through the process of 
measurement. 

3. The process of measuring takes place by 
means of units of magnitude, the units being put 
together till they equal the whole in value. 

4. The idea of number arises in the mind out of 
this process of measuring. 

5. Number is the mind's idea of the times a unit 
of magnitude is applied in the process of measuring. 

"Number is the product of the mere repetition 
of a unit of measurement. " 

Number is the abstract ratio of one quantity to 
another quantity of the same kind. — Newton. 

Number is the ratio of one quantity to another 
quantity taken as a unit. — Euler. 



108 METHOD IN READING AND NUMBER. 

Methods in Use. — There are at any rate the follow- 
ing methods used in primary number work: 1. The 
method of symbols. 2. The fixed unit method; also, 
called the method of things. 3. The Grube method. 
4. The Speer method. 

A brief study of each of these will give some help 
and so will be undertaken. 

The Method of Sijinbols. — This method consists in 
teaching number as merely a set of symbols. It "is 
illustrated in the old-fashioned ways — not yet quite 
obsolete — of teaching addition, subtraction, etc., as 
something to be done with 'figures,' and giving elab- 
orate rules which might guide the doer to certain re- 
sults called 'answers.' It is little more than a blind 
manipulation of number symbols." According to 
this method number is made "the science of figures 
and the art of memorizing and the rules for manipu- 
lating them." 

Many a child has studied arithmetic in this way 
for years without ever having had a right idea of 
number. 

"Wliile the method of symbols is still far too widely 
used in practice, no educationist defends it; aU con- 
demn it. It is not then necessary to dwell upon it 
longer than to point out in the light of the previous 
discussion wJuj it should be condemned. It treats 
number as an independent entity — as something 
apart from the mental activity which produces it ; the 
natural genesis and use of number are ignored, and, 
as a result, the method is mechanical and artificial." 



METHOD IN READING AND NUMBER. 109 

This method subordinates number to the symbol 
of number. The meaning is subordinate to the form ; 
the spirit that maketh alive to the form that killeth. 

This method of merely manipulating figures has 
not one feature to recommend it. 

Illustration. — It used to be the practice to teach 
addition to children by having them to memorize the 
following rule as the first step : 

' Write the numbers to he added so that figures of the 
same order may stand under each other, units under 
units and tens under tens, and draiv a line directly 
beneath. 

Begin at the right hand side and add each column 
separately, writing the units under the column added, 
and carry tens, if any, to the next higher order. At the 
last column write the last whole amount.^ 

After having memorized the rule, the children 
were led to manipulate the figures in the formal 
process of addition according to rule. 

This is an extreme case of teaching according to 
the method of symbols. 

The Fixed Unit Method, or the Method of Things. — 
This method is founded upon the assumption that the 
child gets the idea of number by closely observing 
one object, then another object, and so on. It is 
evident from our previous studies that the child does 
not get his ideas of number in this way, so the funda- 
mental assumption of this method is wrong. 

This method, "the simple perception or observa- 



110 METHOD IN READING AND NUMBER. 

tion method, depends almost wholly upon physical 
operations with things. Objects of various kinds — 
beans, shoe-pegs, splints, chairs, blocks, — are sepa- 
rated and combined in various ways, and true ideas 
of number and of numerical operations are supposed 
necessarily to arise. " 

''The method of things — of observing objects and 
taking vague percepts for definite numerical con- 
cepts — treats number as if it were an inherent prop- 
erty of things in themselves simply w^aiting for the 
mind to grasp it, to 'abstract' it from the things. 
But we have seen that number is in reality a mode of 
measuring value, and that it does not belong to things 
in themselves, but arises in the economical adaptation 
of things to some use or purpose. " 

McLellan and Dewey have the following to say 
about the two methods studied above : 

"Both of these methods are vitiated by the same 
fundamental psychological error; they do not take 
account of the fact that number arises in and through 
the activity of mind in dealing loith objects. The first 
method leaves out the objects entirely, or at least 
makes no reflective and systematic use of them; it 
lays the em^Dhasis on symbols, never showing clearly 
what they symbolize, but leaving it to the chance of 
future experience to put some meaning into empty 
abstractions. The second method brings in the 
objects, but so far as it emphasizes the objects to the 
neglect of the mental activity which uses them, it 



METHOD IN READING AND NUMBER. Ill 

also makes number meaningless; it subordinates 
thought (i. e., mathematical abstraction) to things. 
Practically it may be considered an improvement on 
the first method, because it is not possible to sup- 
press entirely the activity which uses the things for 
the realization of some end ; but whenever this activ- 
ity is made incidental and not important, the method 
comes far short of the intelligence and skill that 
should be had from instruction based on psychologi- 
cal principles." 

This method of things is used largely in almost 
all parts of the country, and since it is so widely 
used, number teaching is far different almost every- 
where from what it should be. The mistake is in pre- 
suming that the child gets the correct idea of one {a unit) 
by closely observing one object. The child's idea of one 
got in this way is qualitative, and not quantitative. 
The child does not see the one as any one employed as 
a quantity with which to measure a larger quantity. 

"A unit is any standard of reference employed 
in counting any collection of objects, or in measuring 
any magnitude. " This is certainly the correct idea 
of a unit numerically considered. 

* The following quotation from McLeUan and 
Dewey will present the chief objection to this method: 

"It (the fixed unit method) does not promote, 
but actually warps, the natural action of the mind in 
the construction of number; it leaves the funda- 
mental numerical operations meaningless, and frac- 



112 METHOD IN READING AND NUMBER. 

tions a frowning hill of difficulty. No amount of 
questioning upon one thing in the vain attempt to 
develop the idea 'one,' no amount of drill on two such 
things or three such things, no amount of artificial 
analysis on the numbers from one to five, can make 
good the ineradicable defects of a beginning which 
actually obstructs the primary mental functions, and 
all but stifies the number instinct." 

The Grube Method. — ''The Grube Method is a 
method of teaching Primary Arithmetic, extensively 
used in Germany. The principle of this method is, 
that it makes each individual number, instead of the 
operations, the basis of the instruction ; and combines 
in each lesson, from the start, the four fundamental 
operations. Thus, in treating the number 2 'all the 
operations possible within the limit of this number' 
are performed in the same lesson. Thus, the child is 
taught that 1+1=2, 2x1 = 2, 2—1 = 1, 2--l = 2, 
2^2 ==1, etc. In teaching the number 4, the lesson is 
1 + 1 + 1+1 = 4, 4—1 = 3, 4X1 = 4, 4^1 = 4; 2+2 = 4, 
2x2 = 4, 4—2=2, 4^2=2; 3+1 = 4, 4-3=1, 3x1+ 
1 = 4, 4-^3 = 1, and 1 remaining, etc. The whole 
circle of operations is exhibited and taught in treating 
each individual number." 

This quotation sets forth pretty clearly the 
essential idea in the Grube Method. It will be seen 
that it starts with a fixed unit, and in principle is not 
substantially different from the Fixed-Unit Method. 
It has all the faults of the Fixed-Unit Method, and so 



METHOD IN READING AND NUMBER. 113 

is subject to all its criticism. The following quota- 
tions will throw some light upon the defects of the 
Grube Method : 

"The unit is never to be taught as a fixed thing 
(e. g., as in the Grube Method), but always as a unit 
of measurement. " 

"We thus see the fundamental fallacy of the 
Grube Method in another light. Just as, upon the 
whole, it proceeds from the mere observations of ob- 
jects instead of from the constructive use of them, 
so it works with fixed units instead of with a whole 
quantity which is measured by the application of a' 
unit of measurement. The superiority of the Grube 
method to some of the other methods, both in the 
way of introducing objects instead of dealing merely 
with numerical symbols, and in the way of systematic 
and definite instead of haphazard and vague work, 
has tended to blind educators to its fundamentally 
bad character, psychologically speaking." 

"According to the Grube method unity is one 
thing and that is the end of it. " 

"Avoid the interest-killing monotony of the 
Grube grind on the three hundred and odd combina- 
tions of half a dozen numbers, which thus substitutes 
sheer mechanical action for the spontaneous activity 
that simultaneously develops numerical ideas and the 
power to retain them. " 

Speer Method. — "The Speer Method in number is 
one that considers number as a r^^tio, and not as 



114 METHOD IN READING AND NUMBER. 

'how many' In the usual meaning of that term. In 
the development of the Speer Method there are three 
stages: (1) The discovery of qualitative relations of 
magnitude, i. e,, that one magnitude is longer or 
shorter, larger or smaller, heavier or hghter, etc., 
than another. (2) The discovery of the quantitative 
relations of magnitude as expressed by their ratios, 
i. e., how many times one magnitude is longer or 
shorter, larger or smaller, heavier or lighter, etc., 
than another, (3) The determination of the plan of 
procedure in the solution of problems from the ratios 
of the magnitude involved." 

The Speer Method may be characterized by say- 
ing it holds closely and consistently to the idea that 
all number work mast deal with the relations between 
magnitudes. It starts by having children to com- 
pare magnitudes and makes the comparison of mag- 
nitudes the organizing idea of all number work. The 
following pages copied from Speer 's "Primary Arith- 
metic" will give some idea of his method of pro- 
cedure. 

Page 65. 

"1. Cut a rectangle into two equal parts. After cutting, 
place the two parts together to see if they are equal. Practise 
cutting and comparing the two parts. 

2. Cut rectangles into three equal parts. Compare the 
parts. Are they equal? jPractise. 

Drawing. — 1. Draw a line. Place a point in the middle 
of the line. Measure to see if the parts are equal. Try 
again. ]\!feasure. Is one of the parts longer than the other? 



METHOD IN READING AND NUMBER, 115 

Are they equal ? What is meant by equal ? Show me one of 
the two equal parts. Show me the other. 

2. Draw a line. Separate it into two equal parts. 
Measure. Are the parts equal? Show me one of the four 
equal parts. Show me three of the four equal parts. Show 
me the four equal parts. 

3. Draw a line. Separate it into three equal parts. 
Measure. Are the parts equal? 

4. Show me where the line should be drawn to separate 
the blackboard into two equal parts. Point to the two equal 
parts of the board. 

5. Can you see the two equal parts of the floor? Of the 
top of your desk? Show me two equal parts of other things 
in the room. 

Give each pupil a square. 

6. Measure the edges of the square. What is true of the 
edges of the square? Find other squares in the room." 

Page 82-84. 

^^ Helations of quart and pint. — show pupils the pint and quart 
measure. Have them find the number of pints equal to a quart by measur- 
ing. 

1. After measuring, tell all you can about the quart and 
the pint. 

2. What is sold by the pint and by the quart? 

3. A quart is how many times as large as a pint? 

4. What part of a quart is as large, or as much, as a 
pint ? 

5. A quart is how much more than a pint? 

6. A pint is how much less than a quart? 

7. A quart and a pint equal how many pints? 

8. Show me li quarts. What have you shown me? 

9. li quarts equal how many pints? 

10. If we call a pint one what ought we to call a quart? 
Why? 



116 METHOD IN READING AND NUMBER. 

11. If we call a quart 2, what ought we to call the sum of 
a quart and a pint? 

12. If a quart is 1, what is a pint? 

Fill the quart and pint measure with water, and let each pupil lift the 
two measures. 

1. Which is heavier, — the quart of water or the pint? 

2. The quart of water is how many times as much as the 
pint? 

3. What part of the quart weighs as much as the pint? 

4. The weight of a pint equals what part of the weight of 
a quart? 

5. The weight of a quart equals the weight of how many 
pints ? 

6. A pint of water weighs a pound; how much does a 
quart of water weigh ? 

7. What part of a quart of water weighs a pound? 

8. The sum of a quart and a pint of water weighs how 
many pounds? 

9. Compare the weight of different solids with the weight 
of a pint of water. 

Ex. : This solid weighs less than a pound, or this solid 
weighs a little more or les^ than a pound. 

10. If a pint of milk costs 3 cts., what ought a quart to 
cost? 

11. In a quart there are how many pints? In three quarts 
there are how many 2-pints? 

12. How much milk should be put into a quart measure to 
make it half full?" 

The ideas of measurement, comparison, and rela- 
tions of magnitude are seen to pervade and dominate 
the whole work. 

WJiat kind of number ivork is it ; good, bad, or in- 
different ? 



METHOD IN READING AND NUMBER. 117 

The Practical Method. — From the various methods 
in use in teaching number the teacher must select a 
hne of procedure possessed of the three following 
characteristics. 

1. The method must be usable by the teacher of 
average intelligence and of average professional prepara- 
tion. 

2. It must be systematic — luell organized and 
definite. 

3. It must as nearly as possible be in harmony 
with the mind's natural mode of action in the develop- 
ment of number ideas and number processes. 

With these three thoughts before us for guidance 
we are ready further to study the method of proceed- 
ing in teaching number. 

The following quotations will give some idea of 
the way to start : 

"The jS.rst lessons in arithmetic should be based 
on the practice of measuring in its varied applica- 
tions." — W. T. Harris. 

"Number grows out of the idea of measurement. 
This should never be forgotten. It is the abstract 
character of so much of the number work that makes 
it uninteresting and unprofitable." — Illinois State 
Course of Study. 

The Two Stages of Number Work. — For the pur- 
pose of helping ourselves in the study of its method 
we may very appropriately divide arithmetic, or 
number, work into two stages, or phases. In a very 



118 METHOD IN READING AND NUMBER. 

general way the first stage consists of about the first 
three years of work which children are accustomed 
to do in school. And this stage may be called primary 
number work. The second stage embraces the re- 
mainder of the learner's work in arithmetic, or num- 
ber, in school, and may be called the advanced stage 
of number work. 

Characteristics of Primary Stage. — This stage of 
number work is characterized by the following : 

1. The work is much more elementary, or sim- 
ple, than that in the second stage. 

2. The work in this stage is to be done best 
without placing any text-books in the hands of the 
pupils. 

3. The work in this stage is much narrower in 
scope than that in the second stage. 

4. The work in the first stage is much more con- 
crete than that in the second stage, that is, the work 
is done more by means of objects. 

Scope of Work in Primary Stage. — In this stage 
the numbers from one to one hundred inclusive are 
dealt with generally. It is fair, perhaps, to say that 
it is customary the country over to confine the num- 
ber work for the first three years of school mainly to 
the numbers from 1 to 100, inclusive. The state 
courses of study for Indiana and Illinois indicate 
approximately what is done in this stage of the work. 

The Uniform Course of Study for Indiana divides 
the first year's work into three parts as follows: 



METHOD IN READING AND NUMBER. 119 

''First Part. — Numbers from 1 to 4, inclusive." 

"Second Part. — Numbers from 5 to 7, inclusive." 

"Third Part. — Numbers from 8 to 10, inclusive, 
and review. " 

The second year 's work is also divided into three 
parts according to this course of study, as follows : 

"First Part. — Numbers from 11 to 13, inclusive, 
as above." 

"Second Part. — Numbers from 14 to 16, inclu- 
sive, as above." 

"Third Part. — Numbers from 17 to 20, inclusive, 
as above, and review. ' ' 

In the third year according to the same course of 
study Cook and Cropsey's New Elementary Arith- 
metic is put into the hands of the pupils, and is to be 
mastered up to and including the 100th page. The 
work in this book up to this place is mainly on num- 
bers below 100 but some work is done on higher 
numbers. 

The Course of Study for the Common Schools of 
Illinois provides for about the same amount of work 
for the first three years as the Indiana Course of 
Study. The work is as follows : 

First Year. — "Number. — From 1 to 10 with com- 
binations. " 

Second Year. — "Number. — Combinations from 
ten to twenty with much concrete work. " 

Third Year. — Arithmetic. — "The work of the 
year includes the mastery of addition and subtrac- 



120 METHOD IN READING AND NUMBER. 

tion, multiplication, division, and partition to 100, and 
the measurement of perimeters and areas. " 

Prom the above it is seen that the first year's 
work in number is spent on the numbers from 1 to 
10, inclusive; that the second year's work is spent on 
the numbers from 11 to 20 inclusive; and that the 
third year's work is mainly spent on the numbers 
from 21 to 100, inclusive, in Indiana and Illinois by 
those who follow the State Courses of Study. And 
since the State Courses of Study are prepared by 
representative educators of these two states they in- 
dicate the consensus of educational opinion more or 
less approximately. 

The object in making the dividing line between 
the first year's work and second year's work at the 
number 10, and between the second year's work and 
the third year's work at the number 20, and between 
the third year's work and the fourth year's work at 
the number 100 is arbitrary, no doubt. There is cer- 
tainly no very good reason for not going further in 
the first year, or further in the second year, or fur- 
ther in the third year, if the ability of the students, 
length of the school year, and progress of the stu- 
dents demand it. To make these divisions of the 
work ironclad is unwarranted either in reason or ex- 
perience. Much just criticism has been given to 
such a division of the work. 

However arbitrary this division of the number 
work may be, it has, however, served a useful pur- 



METHOD IN READING AND NUMBER. 121 

pose. And this purpose is that it has systematized 
and made definite the work of these years. This has 
been useful to teachers and to students. It has 
prevented aimless, fragmentary, disconnected work. 
Indeed, it seems that the thought which gave rise to 
this division of the work was, that the work might 
thus be made systematic, definite, and clear. 

If the scope of the work in the Primary Stage is 
the numbers from 1 to 100, inclusive, the next ques- 
tion is, What is to be done with any individual num- 
ber? What, for instance, is to be done with the num- 
ber 4 in this first stage of the work? In order to 
answer this question we need to study what can be 
known of number, and to this we turn. 

What Can Be Known of a Number. — A careful anal- 
ysis will show that the following may be known of a 
number : 

1. The number as a whole. 

2. The relations in the number. These are as fol- 
lows : 

1 ^ Integral, as follows : 

1^. Any two unequal numbers that make the 
number, as in the following problems : 

If a boy has five marbles and finds four 
more, how many has he? 

If a book costs four dollars and a trunk 
five doUars, what do both cost? 

2^. Any two equal numbers that make the 
number, as in the following problem : 



122 METHOD IN READING AND NUMBER. 

John earns three dollars in a day, and 
James earns the same ; what do both earn ? 

3^. Ally two uneqical numbers into ivliicli the 
number may be separated, as in the following problems : 

John had six pennies and spent two ; how 
many had he left? 

A man spent six of his ten dollars for 
provisions; how many had he left? 

4^. Any two equal numbers into 2vhich the 
number may be separated, as in the following problems : 

A farmer has eight horses and sells four; 
how many has he left ? 

A boy lost five of his ten marbles ; how 
many had he left? 

5^. The number of equal numbers that make 
the member, as in the following problems : 

A man gives two marbles to each of four 
boys; how many marbles does he give? 

A boy leaves two pints of milk at each of 
five houses; how many pints does he leave? 

6^. The number of equal numbers that are 
in the number, as in the following problems : 

A man has eight pints of milk ; how many 
quarts has he? 

A teacher wishes to give ten problems to 
his boys, two to each boy ; to how many boys can he 
give? 

7^. The equal parts of a number, as in the 
following problems : 



METHOD IN READING AND NUMBER. 128 

A man divides eight oranges equally 
among four boys; how many does he give each? 

A stationer distributes nine tablets 
equally among three girls ; how many does each re- 
ceive ? 

21. Fractional, as follows: 

1^. The equal parts of a number, as in the 
following problems : 

A boy had eight marbles and lost four ; 
what part did he lose ? 

A boy had an apple and divided it equally 
among three other boys and himself; what part did 
each have ? 

A farmer had eight horses and six of 
them died; what part died? what part remained 
alive? 

3. Tlie applications of the number. 

1^. Denominate; as, four pecks in a bushel, or 
four gills in a pint. 

2^. General Applications; as, when teaching 
the number 4, the 4's in the room might be pointed 
out by the children. 

4. Tlie notation of the numl)er. 

The symbol of the number may be ( 1) the word 
or words, as eight; (2) the figure, as 8; (3) the Roman 
letters, as VIII. That is to say, the notation of num- 
bers may be by words, figures, or letters. 

Summary. — This may be summed up by saying 
the following may be known of a number : 



124 METHOD IN READING AND NUMBER. 

1 ^ . The number as a whole. 
2^ The relations in it. 
1 2 . Integral. 
22. Fractional. 
3^ Its applications. 
1^. Denominate. 
22. General. 
4^ Its notation. 
What to Do with a Number in the Primary Stage. — 
Prom the foregoing study we see that a number, for 
instance 4, is to be taught (1) as a whole; (2) as to the 
relations in it, both integral and fractional; (3) as to 
its applications, both denominate and general, and (4) 
as to its notation. This work is to be done with each 
number from 1 to 10, inclusive, in the first year; 
from 11 to 20, inclusive, in the second year, and from 
21 to 100, inclusive, in the third year. Each of these 
points will repay further study. 

The Number as a Whole. — When does the learner 
know the number as a whole, and how proceed in 
teaching it? In answer to this question, the learner 
knows a number as a whole when he knows it as made 
up of so many ones, or again, he knows it as a whole 
when he knows it as made up of the next number beloiv 
it and one. Thus the learner knows the number 4 as 
a whole when he knows it as made up of four ones, or 
when he knows it as made up of three and 07ie. And 
in answer to the second part of the question, one term 
in the above needs to be studied, and this is the one. 



METHOD IN READING AND NUMBER. 125 

The One, or the Measuring Unit. — The one in num- 
ber is not a fixed quantity, but is relative. It indi- 
cates that something taken as a measuring unit has 
been apphed to some unmeasured whole once. Thus 
the one is anything — one inch, one mile, one week, 
one century, one ounce, one ton, one tree, one boy, 
one book, one flower — employed as a unit of measure. 

The perennial dispute as to whether one is a 
number seems out of place when this view of one is 
taken. 

This idea of what the one is furnishes guidance in 
teaching a number as a whole; that is, it indicates 
that the teaching must be done so as to lead the child 
to see that the ones are so many applications of the 
measuring unit. This may be done as follows : 

If the number to be taught be four, draw a line 
on the board four feet long; give the child a foot 
measure and have him measure off three feet, then 
one more and ask him how long the line is. If he 
does not know the name of the new number it will 
have to be given him. Or give the child a pint cup 
and have him measure three pints of water and put 
them in a bucket, then one more and ask how many 
pints of water are in the bucket. Then ask him to 
show fours of things in the room, or on the table, or 
tell fours of things he has seen at home or on the 
road to school. Repeat this kind of work until the 
learner has the idea of four as a whole weU in mind. 



126 METHOD IN READING AND NUMBER. 

The work with any of the other numbers as a 
whole is to be done in a similar manner. 

The Relations in the Number. — From the study of 
the nature of number, and from the study of the 
meaning of one, we also get knowledge valuable for 
guidance in teaching the relations in number. These 
studies indicate that these relations shall be taught 
in such a way as to lead the learner to see that num- 
ber is always the result of measurement. The 
measuring idea is always to be made prominent. 

In order to make clear the meaning of the inte- 
gral relations in a number, let us arrange the relations 
in the number 4, as follows : 

1. Three and one. 

2. One and three. 

3. Four minus one. 

4. Four minus three. 

5. Two and two. 

6. Four minus two. 

7. Four divided by two. 

8. Two twos. 

9. Four minus four. 

10. Four divided by one. 

11. Four ones. 

It readily appears that these relations divide 
themselves into synthetic and analytic relations. 
The synthetic are : 

1. Three and one. 

2. One and three. 



METHOD IN READING AND NUMBER. 127 

3. Two and two. 

4. Two twos. 

5. Pour ones. 
The analytic are : 

1. Pour minus one. 

2. Pour minus three. 

3. Four minus two. 

4. Pour divided by two. 

5. Pour minus four. 

6. Pour divided by one. 

It is also evident that addition, subtraction, multi- 
plication, and division are all employed in working out 
the relations in any number. 

Now since these relations are to be taught, the 
question, What shall be the order of teaching the re- 
lations? arises. McLeUan and Dewey say very 
pointedly that the relations involving addition and 
subtraction should be taught first; secondly, the re- 
lations invoMng multiplication ; and, lastly, those in- 
volving di\ision. The following wiU show their 
thought: "The psychological order as determined 
by the demand on conscious attention is the old-time 
arrangement — Addition and Subtraction, Multiplica- 
tion and Division. 

It is the order in which numerical ideas and 
processes appear in the evolution of number as the in- 
strument of measurement; the order in which they 
appear in the reflective consciousness of the child; 
the order of increasing growth in psychological com- 
plexity. " 



128 METHOD IN READING AND NUMBER. 

From the foregoing study, in teaching the rela- 
tions in a number, the teacher holds in mind a given 
relation, and so manipulates objects or has the chil- 
dren so manipulate them as to lead them to grasp the 
relation and state it. In this work the idea of meas- 
urement is made prominent, and the order of the re 
lations is, first, addition and subtraction; secondly, 
multiplication and division. 

Help will come from arranging the fractional re- 
lations of some number, as of the number 4. They 
are : 

1. Three fourths of four and one fourth of four. 

2. One fourth of four and three fourths of four. 

3. Four minus three fourths of four. 

4. Four minus one fourth of four, 

5. Two fourths of four and two fourths of four. 

6. Four minus two fourths of four. 

7. Four divided by two fourths of four. 

8. Two two fourths of four. 

9. Four minus four fourths of four. 

10. Four divided by one fourth of four. 

11. Four one fourths of four. 

The Applications of a Number. — Upon taking up 
the study of the applications of a number two kinds 
of applications will be studied. 

1. The applications of a number in the tables; 
that is, the denominate applications. 

2. The applications of a number in general. 
Under the first the children are to be taught con- 



METHOD IN READING AND NUMBER. 129 

cretely in connection with any number all the units 
of the tables, which consist of that number ; as : 
Four inches are one hand. 
Pour gills are one pint. 
Four pecks are one bushel, etc. 
The denominate applications of numbers from 1 
to 10 are : 

1. 
One cent. 

2. 
Two one -cents are two cents. 
Two pints are one quart. 
Two reams are one bundle. 
A sheet folded into two leaves is a folio. 

3. 
Three feet are one yard. 
Three feet are one pace. 
Three miles are one league. 
Three one-cents are three cents. 

4. 
Four quarters are one yard. 
Four quarters are one dollar. 
Four inches are one hand. 
Four gills are one pint. 
Four pecks are one bushel. 
Four quarts are one gallon. 
Four weeks are one month. 
Four farthings are one penny. 
A sheet folded into four leaves is a quarto. 



130 METHOD IN READING AND NUMBER. 

5. 

Five one cents are five cents. 
6. 

Six feet are one fathom. 
/. 

Seven days are one week. 
8. 

Eight quarts are one peek. 

Eight cord feet are one cord. 

A sheet folded into eight leaves is an octavo. 
9. 

Nine square feet are one square yard. 
10. 

Ten cents are one dime. 

Ten dimes are one dollar. 

Ten dollars are one eagle. 

Under the general applications of a number, the 
pupils are required to solve, and to form and solve 
miscellaneous problems ; as : 

If a boy buys three apples at one store and one 
at another store, how many does he buy ? 

If a man has four oranges, to how many boys 
can he give two each? 

Notation of the Number. — Notation may be defined 
as the science and art of representing numbers by 
symbols. The symbols used are words, letters and 
figures. Thus the number 4 may be symbolized by 
{l)four; (2) by IV; and (3) by 4. The first kind of 
notation may be called notation by 2uords; the second 



METHOD IN READING AND NUMBER. 131 

is called the Roman notation; and the third, the 
Arabic notation. 

At some time during the first three years the 
notation of numbers from 1 to 100 is taught. 



CHAPTER X. 

METHOD OF PROCEDURE IN TEACHING NUMBER.— 

CONCLUDED. 

The Primary Stage. — In an approximately accu- 
rate way it may be said that in the primary stage of 
number work, the numbers from 1 to 100, inclusive, 
are to be taught, each (1) as a whole; (2) as to the in- 
tegral and fractional relations in it ; ( 3 ) as to its de- 
nominate and general applications; and (4) as to its 
notation. Now, this must be understood to mean 
that most of the work falls within this scope, but that 
it is not of necessity limited to this scope. 

Thine of Beginning. — There are good reasons for 
believing it best not to start the child on the number 
work proper at the beginning of the first year, but 
that the number work for the first two or three 
months should be incidental. The following shows 
one author's thought : 

"The work during a period of about three months 
in so far as number is concerned is incidental. 

The main idea is to train the mind by a considera- 
tion of form, as sphere, cube, cylinder, prism, square, 
triangle, points, etc. 

In doing this work number is, of necessity, inci- 
dentally introduced and learned. " 



METHOD IN READING AND NUMBER. 133 

The nature of this work may be seen from the 
following : 

1. ''What is this? 

Find other balls, or spheres. 

Find a larger sphere than this. Find smaller 
ones. 

2. Name objects like a sphere. * * * * 

3. What is the largest sphere that you have 
seen? 

What is one of the smallest spheres that you have 
seen? 

4. To-morrow tell me the names of spheres that 
you see when going from school and at home. 

5. What was the largest sphere you found? 
What was the smallest?" 

Finding Colors. — Tests in color should be given before the 
formal work suggested below. For example: Group cards 
of the same color and threads of worsted. 

Provide ribbons, worsted, cards, etc., of different colors, 
to be found by pupils when looking for a particular color. 

Pin or paste squares of standard red and orange where 
they can be seen. Pin the red above the orange. 

1. Find things in the room of the same color as 
the red square. What things can you recall that are 
red? 

2. Look at the orange square. Find the same 
color elsewhere in the room. Recall objects that 
have this color. 



134 METHOD IN READING AND NUMBER. 

3. Close your eyes, and picture, or image, the 
red square. Now the orange square. 

4. Which square is above? Which below? 
Name the two colors. 

5. To-morrow bring something that is red and 
something that is orange. Also tell the names of 
orange or red objects that you see in going to and 
from school. 

Pin or paste a square of yellow below the orange. 

1. Look at the yellow. Find the same color in 
the room. Recall objects having this color. 

2. Look at the red, then the orange, then the 
yellow. Close the eyes and picture the colors one 
after another in the same order. 

Cover the squares. 

3. Wliich color is at the top? At the bottom? 
In the middle? 

4. Name the three, beginning at the top. Name 
from the bottom. 

5. Wliich color is third from the top? Second 
from the top? Third from the bottom? 

6. To-morrow bring something that is yellow 
and tell me the names of things that you have seen 
that are yellow. 

Add a square of green. 

1. Find green. Recall objects that are green. 

2. Try to see the green square with the eyes 
closed. 

3. Look at the four colors. 



METHOD IN READING AND NUMBER. 135 

4. Think of the fouy, one after another, with the 
eyes closed. 

Cover the squares. 

5. Think the colors slowly from the top down. 
From the bottom up. 

6. Name the colors from the top down. From 
the bottom up. Which is second from the top? 
Third from the bottom? Second from the bottom? 

7. Which color do you like best ? ' ' 

Lessons similar in character may be given on 
magnitudes — the cube, the cylinder, the square, the 
oblong, the triangle, the circle, the line, the cone, the 
prism, etc., the teacher constantly emphasizing sense 
training and the comparison of magnitudes. 

The Number as a Whole. — It will be recalled that 
the child knows a number as a whole when he knows 
it as made up of so many ones, or as made up of the 
first number below it and one. And so when the 
learner is led to see this he has been taught the num- 
ber as a whole. 

Illustration. — If the child is to be taught the num- 
ber 7 as a whole, we can assume that he knows the 
number 6. Then we may give him a number of cubes 
and have him to put six in one place, and one in 
another place ; then have him put them all together, 
and then ask him how many he has. If he does not 
know the name of the new number, it should be given 
him. Next he may put six counters in one place and 
one in another place, then put them together and tell 



136 METHOD IN READING AND NUMBER. 

the "story." The story is, six counters and one 
counter are seven counters. 

The "story " is a term the child is to be taught 
from the fitst, just as a matter of convenieDce in 
teaching number. The child will learn it at first by 
imitation, but he wUl soon grasp its significance. 

Further Illustration. — More in accord with the 
idea that number results from measurement is the 
following : Draw a line on the board. Give the child 
a foot rule and tell him to measure off six feet, then 
another foot. Ask him how many feet he measured 
off. Have him tell the story. It is, six feet and one 
foot are seven feet. Or have the child cut a paper slip 
six inches long, then another one inch longer. Have 
him tell the story. 

The Relations in a Nurriber. — In teaching the rela- 
tions in a number the integral relations should be 
taught first and then those involving fractions. 
These are to be taught concretely ; that is, by means 
of objects, first. There are, though, really three 
stages in teaching each relation. And these stages 
are as follows : 

1. The teaching of the relation in the presence 
of the objects. This is called the sense-preception 
stage. 

2. The teaching of the relation in connection 
with objects, though the objects are not present. 
This is called the imagination stage. 



METHOD IN READING AND NUMBER. 137 

3. The teaching of the relation without objects ; 
that is, abstractly. This is called the abstract stage. 

Illustration. — Suppose the relation is 4 and 3 are 
7. The teacher has the child to measure off four 
inches of a line, then three more and asks how many- 
inches have been measured off ; or she has the child 
to put four counters in one place and three in another, 
then all together and asks how many. This is con- 
crete teaching in the sense-perception stage, because 
the sensuous material is handled by the children as a 
means in leading them to see the relations in the 
number. 

After having taught the relation, 4 and 3, in this 
way, the teacher might give the following problem : 
Three birds are sitting on the fence and four in a 
tree ; if those on the fence should fly into the tree, 
how many would there be in the tree? Or, a farmer 
has four bushels of corn in a box and three bushels 
in a barrel; how many bushels has he in both the box 
and the barrel? 

In these cases the objects are not present, but 
the child pictures them in his imagination. This is 
teaching the relation in the imagination stage. 

But suppose the teacher says to the child 4 and 
3 are how many? or, 3 and 4 are how many? the work 
is purely abstract, and such teaching is in the ab- 
stract stage. 

Importance of Each. — The work is important in 
each of these three phases of teaching the relations 



138 METHOD IN READING AND NUMBER. 

in primary number, and should be intelligently and 
systematically done. 

The first is important because it appeals to the 
senses of the child, is interesting, and lays a sure 
foundation for the other two kinds of teaching. 

But the child must learn to think when not in the 
presence of the objects about which he is thinking. 
If one were able to think only in the presence of ob- 
jects he would be a slave to his environment; he would 
belong more to the world of things around him than 
to himself. So the child needs the work in the imag- 
ination stage in order to learn to picture the condi- 
tions of problems. And this he needs to learn to do 
well. 

The child needs work in the abstract stage in 
order to become skillful in thinking number relations. 
When 4 and 3 are presented to the mind it is desir- 
able that 7 come into the child 's mind as quick as a 
flash. And the same thing is desirable concerning 
other numbers. In order to make the child skillfid 
in seizing the relations in numbers thus, he must have 
much of this abstract work. 

Thoroughness of Work. — In working with any 
number, as with the number 6, it is not only not nec- 
essary to exhaust the number before taking up the 
relations in the next number, but not even desirable. 
To exhaust one number before beginning with the 
next is to deal with numbers as isolated to too great 
an extent. Such teaching does not sufficiently em- 



METHOD IN READING AND NUMBER. 139 

phasize the relations between numbers. It further 
keeps the child upon one thing until it becomes mo- 
notonous and uninteresting to him. 

The work in dealing with the most important re- 
lations in numbers from 1 to 100 must be varied suffi- 
ciently to maintain interest, but must be repeated often 
enough for the child to so thoroughly fix them in mind 
that they will come into his consciousness instantaneously 
when needed. Nothing is more annoying than for the 
child to have to stop and count his fingers, or dots, or 
some other objects in order to know, for instance, 
how many 8 and 9 are. 

Fractional Relations. — The work in teaching frac- 
tional relations should keep pace approximately with 
the work in teaching the integral relations. That is 
to say, if, for instance, the integral relations in the 
number 4 are being taught, before leaving the num- 
ber the fractional relations are to be presented 
through the three stages — the sense-perception 
stage, the imagination stage, and the abstract stage 
— as in teaching the integral relations. 

Illustration. — In starting this work an apple may 
be separated by a pupil or the teacher into two equal 
parts, the children being led to see that the parts are 
equal. Then they are giv^n the name for the parts, 
if they do not already know it. After they learn the 
name, one-half the pupils are led to see the following : 

One-half and one-half are one. 

One less one-half is one-half. 



140 METHOD IN READING AND NUMBER. 

Two one -halves are one. 
In one there are two halves. 
One-half of one is one-half. 

In teaching the fractional relations of the num- 
ber 3 there are two steps : 

1. The teaching of the idea, one-third. 

2. The teaching of the thirds of three. 

The idea, one-third, is to be taught as foUows : 

Give a child a paper three inches long and teU 
him to cut it into three equal parts. Then teach him 
that each part is called one-third; then as follows : 

One-third and two-thirds are one. 

Two-thirds and one-third are one. 

One less two-thirds is one-third. 

One less one-third is two-thirds. 

Three one-thirds are one. 

In one there are three one-thirds. 

One-third of one is one-third. 

Two-thirds of one is two oae-thirds. 

In teaching the thirds of three the procedure is 
as follows : 

Give the learner three cubes and tell him to show 
you one-third of them. Then have him tell the story. 
It is, one third of three cubes is one cube. Then the 
child is to be led to see : 

One-third of three is one one. 

Two-thirds of three is two ones. 

Three- thirds of three is three ones. 

One is one-third of three. 



MEGTHOD In REAOTNG ANlJ NUMBER. 141 

Two are two-thirds of three. 

Three are three-thirds of three. 

The procedure in teaching the fractional rela- 
tions of other numbers is to be the same as in the 
teaching of tioo and three. 

Important and Unimportant Relations. — There are 
numbers whose relations, both integral and frac- 
tional, are of much less importance than those of 
some other numbers. Thus 13, 17, 19, 23, 29, 31, 37, 
41, 43 and 47 are some of these numbers, while 10, 
12, 14, 15, 16, 18, 20, 21, 24 and 36 are among the more 
important. 

In teaching these less important numbers it 
would not be necessary nor desirable to teach "all 
the possible relations " in them. It would not be de- 
sirable to spend much time on |, |, J, §, i? t? i? ©tc, 
of 13, but one should teach the thirteenths of 13. 
Likewise in teaching 16, it would not be desirable to 
teach the thirds, fifths, sixths, sevenths, ninths, 
tenths, elevenths, twelfths, etc., of 16, but it would 
be desirable to teach the halves, the fourths, the 
eighths and the sixteenths of 16. 

The Measuring Idea. — By way of emphasis we are 
justified in repeating that every reasonable effort 
should be made to keep before the child's mind the 
idea that number is a result of measurement. So in 
teaching relations in numbers this idea should per- 
vade the whole work. 

The Denominate Applications. — By denominate ap- 



142 METHOD IN READING AND NUMBER. 

plications are meant the units of the tables consisting 
of the various numbers, as 8 quarts are one peck, or 
4 gills are one pint. These are to be taught con- 
cretely in connection with the various numbers. 

Illustration. — Thus in teaching the number 2, one 
denominate application to be taught is, two pints are 
one quart. In teaching this concretely the teacher 
secures a quart measure, a pint measure, and some- 
thing to measure. She has a child to take the pint 
measure and fill the quart measure, noting how many 
pints it requires. Then the quart measure is filled 
and emptied into the pint measure, the child noting 
how many times it fills the pint. In each case the 
story is asked for. In the first case the story is, tivo 
pints of water are one quart. In the second case the 
story is, in one quart of water are two pints. 

The other denominate applications of two and of 
the other numbers are to be taught in a similar way, 
when possible. All are to be made as nearly con- 
crete as possible. 

The Generjal Ajyplications. — General applications 
are simply those in the solution of problems found in 
life. There is no more important part of number 
work than these problems. A teacher's success in 
teaching number will depend largely upon his ability 
to give his pupils many good problems — problems not 
too hard and not too easy. Those that will constantly 
lead the child to a little stronger thinking. 

In connection with every number many of these 



MET^HOD IN READING AND NUMBER. 143 

little problems should be solved by the students. In 
this work there is rare opportunity for the teacher 
to show her skill in leading the pupils to think for 
themselves. And the learner's growth in applying 
number to the solution of problems arising in practi- 
cal life depends almost wholly upon how well the 
teacher does this work in general ajjplications. 

It is oftentimes a very heavy task upon teachers 
to arrange these problems originally for their pupils. 
This task may be made lighter on teachers by their 
securing some good teachers' manuals on number, or 
primary arithmetiQ. These contain large numbers 
of problems from which the teacher may draw. 

A list of such books will be found at the end of 
this chapter. 

Illustrations. — Suppose the number under con- 
sideration is 21. The following are some of the prob- 
lems suitable to the children in the average class in 
this stage of the work : 

1. Some birds were in a tree; 7, which was i of 
them, flew away. How many were there at first? 

2. A man sold 14 sheep, which was | of what he 
had at first. How many had he at first? 

3. A gardener takes 21 bushels of apples to 
market, and sells | of them. How many does he sell? 
How many has he left? 

4. A man gave 3 children 7 apples each; how 
many did he give to them all? 

5. A little girl has 21 picture cards to give to 



144 



METHOD IN READING AND NUMBER. 



her playmates. To how many can she give them, if 
she gives 3 to each ? 

6. 4 of 21 are how many? 

7. f of 21 are how many ? 

8. J and I of 21 are how many? 

Picturing Problems. — This is work to be done by 
the children at their seats or at the board. 
The following will illustrate : 
1. How many 4 spheres in 16 spheres ? 




2. I have 20 cents to spend for picture cards; if 
I pay 4 cents apiece, how many can I buy ? 

10 




OS) QO OS) QgopQ_qos) QOO^ 

This is valuable to children in helping them to 
see the relations in their problems in the earlier 
stages of the work. It is easily abused, though, and 



kEinOD IN READING AND ISfUMBER. 145 

carried to extremes. The child should reach a place 
as soon as possible where he can solve the little prob- 
lems without the pictures. To carry this work too 
far would not foster rapidity of thought. As a de- 
vice, though, properly used it is very helpful to chil- 
dren, and it lightens the work of the teacher. 

Notation. — Notation may be defined as systematic 
number representation. There are three kinds : ( 1 ) 
notation by means of words; (2) Roman notation; 
and (3) the Arabic notation. These are all in use 
more or less, but the most use is made of the Arabic 
in teaching number. 

There is a question concerning when to begin 
teaching notation, worthy of some study. Some say 
that the notation of numbers should be taught as soon 
as the child has ideas of number. And by this is 
meant that figures are to be taught as soon as the 
number work begins. Others would not teach nota- 
tion before the beginning of the second year. One 
author says: "The fundamental defect in dealing 
with arithmetic is that expression is treated instead of 
number. 

This manifests itself in various ways : 

1. In the failure to teach the ideas and oral terms 
of numbers for a considerable time before beginning the 
work on written symbols. In reading, the child has 
been dealing with ideas and oral terms for six or 
more years before he begins work upon the written 
word." 



146 METHOD IN READING AND NUMBER. 

This author, who is a most excellent thinker 
would not teach the figures before the beginning of 
the second year. 

The one objection against teaching the Roman, 
and the Arabic notation during the first year is, that 
it is difficult to prevent the child from getting a ivrong 
conception of number — the conception that the figures are 
the members. 

The point in favor of it is, that it is convenient in 
teaching to have the child know the figures the first 
year, and since he must know them some time, it is 
just as well to teach them as soon as he gets the num- 
ber ideas. 

It is indeed very unfortunate for the child to get 
the notion that the figures are the numbers, and every 
reasonable effort should be made to prevent such a 
mistake. So, unless the teacher be exceedingly skill- 
ful, it is no doubt better not to teach notation till the 
beginning of the second year. 

Two Stages. — There are two stages in the process 
of teaching notation to children. The first consists 
of the teaching of the notation of the numbers from 1 
to 9, inclusive ; the second consists of the notation of 
numbers from 10 to infinity. 

The First Stage. — The first stage is very simple, 
and offers very little difficulty in teaching. If nota- 
tion is not taught until the second year, the following 
is a good way to proceed : 

Draw a line on the board. Tell the child to 



METHOD IN READING AND NUMBER. 147 

measure off six inches. Tell him you are going to 
place on the board what makes you think six. Write 
the figure 6 on the board. Tell him to measure one 
more inch, and you will write what stands for it. 
Write the figure 7. Or teU him to erase one inch and 
you will write what stands for what is left, etc. 

Point to the figure 6 and let him measure off the 
number, or point to 5 or 7 and let him measure. 

It is evident that this process is much like teach- 
ing words as standing for their ideas in reading, and 
the steps are in general the same. They are : 

1. The -advance of the mind in rethinking the 
old number. 

2. The advance of the mind in adjusting itself to 
the figure. 

3. The advance of the mind in making the asso- 
ciation between the figure and the number. 

The following devices will help to make the asso- 
ciation strong. 

00 000 0000 00000 000000 0000000 

12 3 4 5 6 7 

00000000 000000000 

8 9. 

00 000 0000 00000 000000 0000000 

one two three four five six seven 

I. XL III. IV. V. VI. VII. 

12 3 4 5 6 7 

00000000 000000000 
eight nine 

VIII. IX. 

8 9 



148 METHOD IN READING AND NUMBER. 

The Second Stage. — This is the stage which offers 
difficulty in teaching, and the teaching well of the 
work in this stage is of tremendous importance. 

In order to form a good basis to work upon here 
it is well to teach the notation of ten, eleven and twelve 
in the same way as the notation of numbers from one 
to nine w^ere taught. Then one can proceed to teach 
the principles underlying the notation of these num- 
bers. We want the child to see : 

1. That the one ten resembles the one unit in 
being a one, but that it differs from it in value. 

2. That therefore its symbol should be like that 
for one unit and different from it. 

3. That the same symbol is used, but that it is 
different in being held in the second place by some figure 
to its right. 

4. That the difference in value expressed by a 
figure is because of its position. 

5. That the first place is ones', or units' placCf 
and the second is tens' place. 

The following will indicate how to proceed in 
teaching : Give the child twelve counters. Ask him 
how many ones in twelve. Tell him to show you how 
many tens in twelve and how many ones over. Ask 
him to write 12 on the board. Ask him if he can see 
what the figure 2 means ; what the figure 1 means. 
He will readily see that the 2 means two ones, and 
that the 1 means one ten. 



METHOD IN READING AND NUMBER. 149 

Teach eleven in the same way, using eleven 
counters. 

Have the child write 10 on the board. Ask him 
what the 1 means ; what the means ; why it is used. 

Ask him if he can now tell you where ones' place 
is in writing number ; where ten's place is. 

From this the child should be able to write 13, 
14, 15, 16, etc., and teU why he writes them so. If 
he should have difficulty, work out some more of 
them concretely; that is, with the counters. 

The next point of difficulty wiU be in the notation 
of one hundred and numbers above it. 

One hundred may be worked out concretely as 
follows: Give the child 100 counters. Have him 
divide them into tens by putting little rubber bands 
around each ten. Have him make them into one 
hundred by putting a rubber band around the ten 
tens. Show him he has no tens nor ones to write 
when he has written the 1 one-hundred. Ask him 
what to put in tens' place, what in ones' place. 

The average child will readily see the notation of 
one hundred thus. 

Importance of Plastering Notdt ion.— The notation 
of numbers both in the science and art phase simply 
must be mastered in primary number work. The 
teacher can make no worse mistake in teaching num- 
ber than to fail to have students thoroughly to under- 
stand notation. It is an impossiMlity to teach students 
ivell the formal processes of addition^ suUraction, multi- 



150 METHOD IN READING AND NUMBER. 

plk'ution, and division, if they have not a good under- 
standing of notation. Let the student have well in 
mind notation, and the teaching of the formal proc- 
esses of addition, subtraction, multiplication, and 
division becomes easy. The importance of notation is 
not likely to be too strongly emphasized. 

EniDneration. — Enumeration is the reading of 
number symbols. Some attention will have to be 
given this in connection with notation. It offers no 
special difficulty, if notation is well taught. 

The Multiplication Table. — The question, When and 
how teach the multiplication table? is one worthy of 
some study. Many have felt that the old-fashioned 
way of memorizing it by rote is a very poor way to 
teach it, and it certainly does kill interest and waste 
time and energy. 

It is evident that if, at the end of the third year, 
the child has mastered the relations in the numbers 
up to and including one hundred, he has mastered the 
multiplication table. For instance, in dealing with 
four, he learns that 2x2 = 4; in dealing with six, he 
learns that 2x3 = 6; in dealing with eight, that 2x4= 
8; in dealing with ten, that 2x5 = 10: in dealing with 
twelve, that 2x6=12, and so on. In a similar way he 
has learned in dealing with six, that 3x2=6; in deal- 
ing with nine, that 3x3 = 9; in dealing with twelve, 
that 3x4 = 12; in dealing with fifteen, that 3x5 = 15, 
and so on. And thus with the numbers, for example, 
nine. In dealing with nine he learns that 1x9 = 9; in 



METHOD IN READING AND NUMBER. 151 

dealing with eighteen, that 2x9 = 18; in deaUng with 
twenty-seven, that 3x9 = 27; in deahng with thirty- 
six, that 4x9 = 36, and so on. 

Prom this the hint may be had that the multiph- 
cation table is to be taught in connection with the 
various numbers throughout the entire first three 
years of the number work. 

This does not mean that the multiplication table 
is to he taught incideiitally : for to teach a thing incident- 
ally usually means to make it of secondary importance 
and, therefore, to slight it. The multiplication table 
must not be slighted. 

The teacher may set about to teach it systematic- 
ally as follows : 

In teaching, for instance, twelve, the table of twos 
should be learned to twelve ; the table of threes, the 
table of fours, and the table of sixes also should be 
learned to twelve. 

In teaching twenty-four, the table of twos, the 
table of threes, the table of fours, the table of sixes, 
and the table of eights should be learned. 

In teaching thirty- six, the table of threes, the 
table of fours, the table of sixes, and the table of nines 
should be learned. 

In teaching fifty-six, the table of sevens, and the 
table of eights should be learned. 

Enough numbers have been given to show the 
nature of the work. All other numbers involving the 
tables should be taught in the same manner. 



152 



METHOD IN READING AND NUMBER. 



It is evident that if this work is carefully done, 
that the opportunities for reviewing the tables are so 
many that the child will almost surely learn them 
well. There is, too, a gradual growth, which will 
lessen the burden of memorizing. 

Much drill should be given in order that the asso- 
ciation may not be successive. It is very annoying 
if, for instance, when the child wants to know 7x7, 
he must repeat the table of sevens up to that place to 
get the number 49. It is desirable for 49 to come 
into his consciousness instantly when he wants the 
product of 7x7. The following device is helpful in 
this work : 




The seven in the center of the circle may be 
changed to 2, 3, 4, 5, 6, 8, or 9. 

Teachers' Helps. — The following are among the 
most helpful books for teachers on the subject of pri- 
mary number : 



METHOD IN READIKG AND NUMBER. 153 

1. Wentworth and Reed's Primary Arithmetic, 
Ginn and Co. , Chicago. 

2. Cook and Cropsey's Elementary Arithmetic, 
Parts I. and II., Silver, Burdett and Co., Chicago. 

3. Speer's Primary Arithmetic, Parts I. and II., 
Ginn and Co., Chicago. 

4. Pierce's First Steps in Arithmetic, Silver, 
Burdett and Co., Chicago. 

5. The Werner Arithmetic, Book I., the Werner 
Co., Chicago. 



CHAPTER XI. 

PROCEDURE IN THE SECOND STAGE. 

General Scope. — In this stage of number, or arith- 
metic, work, is included all the work the child does in 
school in arithmetic beyond the work in what has been 
called the primary stage. In this stage are to be 
taught the formal processes of addition, subtraction, 
multiplication and division. An intense study of denomi- 
nate numbers is to be made. Fractions both common 
and decimal, percentage in its applications, ratio, pro- 
portion, etc., are also taught. 

It will be our purpose to study the method of only 
the elementary parts of this work. The method of 
the advanced parts of arithmetic, however valuable, is 
beyond the scope of the present studies. 

TJte Formal Process of Addition. — The child has been 
dealing with addition for something near three years 
now, but not as a formal process. This will not be 
difficult for him now. 

There are two stages in teaching this, as follows : 

1. The teaching of those problems in which the 
sum of the addends in any order does not equal ten. 

2. The teaching of those problems in which the 
sum of the addends in any order equals or exceeds ten. 



Method in reading and number. 155 

123+234+522 illustrates with a problem in the 
first stage, and 2896+8637+231 iUustrates with a 
problem in the second stage. 

The First Stage. — This is quite simple, and easily 
taught, because it does not involve the idea of reduc- 
tion. The method of teaching is as follows : Send 
the pupil to the board and tell him to write twenty- 
five ; then tell him to write under twenty-five thirty- 
two. Ask him to add the five and the two. Ask him 
what his five is, and what his two is ; then what his 
seven is. Tell him to write the seven where he thinks 
it belongs. If he does not get it in the right place, 
show him where it is customary to write it. Now lead 
him to see by questions that the two and three are 
tens. Have him add them, and ask if he knows where 
to write the five and why. Then ask him how many 
twenty-five and thirty -two are. 

If the child understands this problem, he will 
solve the next one without help. Give him a goodly 
number to fix well in mind the form of such problems. 

The Second Stage. — This stage is more complex 
and offers more difficulty in teaching, because, it 
involves the idea of reduction. The method of teach- 
ing is as follows : 

Tell the pupil to write on the board or slate or 
note book fifty -six. TeU him to add to it thirty-four. 
Lead him by questions to see that the six and the four 
are ones ; then that their sum is ten ones. Lead him 
to see that his one is one ten and must be put in tens 



156 METHOD IN READING AND NUMBER. 

place, and that he has only naught to put in ones' 
place. Let him write the one in tens' place and the 
naught in ones' place. Lead him by questions to see 
that the five and the three are tens; that their sum is 
eight tens. Let him write it in tens' place. Then 
show him that for convenience the one ten is not writ- 
ten but held in mind and added to the three and the 
five tens, and the sum of them all is written. 

From this start problems gradually increasing in 
length and difficulty are given and solved, the reason 
for each step being obtained from the students by the 
questions of the teacher. 

A place will soon be reached where it will be 
desirable to give the names and work out the meaning 
of the terms — addend and sum — used in addition; also 
the principle that only like numbers can be added. 
These if taught in the best way possible, will be 
taught inductively. 

It is to be noted that the old erroneous notion of 
"carrying to the next higher order" is entirely unnec- 
essary, and easily avoided when addition is rightly 
taught. 

The Formal Process of Subtraction. — The learner 
has been solving subtraction problems for three years 
now, but not the formal process of subtraction. Hav- 
ing learned notation well he now has a good basis for 
subtraction as a formal process. 

As in addition, there are two stages in teaching 
this process, as follows : 



METHOD IN READING AND NUMBER. 157 

1. The stage in which those problems in the sub- 
trahend of which the number in any order is smaUer 
than the number in the minuend in the same order, 
are taught. 

2. The stage in which those problems whose 
minuend has a number in any order smaller than the 
number in the same order of the subtrahend. 

4867 — 2534 illustrates with a problem of the first 
stage,- and 2365—1758 illustrates with a problem of 
the second stage. 

TJie First Stage.— This stage offers very little or 
no difficulty in teaching because of its simplicity. 
The method of teaching it is something as follows : 

Let the pupil write on the board or his slate or on 
note paper, for instance, 875 and under it 352 and teU 
him to subtract one from the other and write the re- 
sult where it should be written. From what he has 
learned in notation and addition he will almost surely 
catch the idea in the first problem. Then all that is 
necessary is to give him a number of problems grad- 
uaUy increasing in difficulty. 

The Second Stage.— In this stage the pupil will 
encounter a real difficulty, because it is made some- 
what complex by the reduction involved. 

The method of teaching should be somewhat as 
follows : Tell the student to place 34 on the board 
and subtract 18 from it. He will know that 18 
may be taken from 34, but he comes face to face 
with a difficulty to start with; namely, he can 



158 METHOD IN READING AND NUMBER. 

not take 8 from 4. The teacher now may lead the 
child to see what to do, concretely. Give the learner 
34 counters, and tell him to make them into tens. He 
makes them into 3 tens and places a rubber band 
around each ten. Lead him to see that the 34 is the 
symbol of the 3 tens and 4 ones. Now ask him to take 
away 8 one-counters. In order to do this he must 
change 1 ten-counters into ones. Then ask him how 
many tens he has and how many ones. Have him re- 
move the 8 ones, and write on the board the number 
of ones he has left. Ask him how many tens he has 
left. Tell him to take away one ten and write on the 
board the number of tens he has left. 

In this concrete way the pupil learns that when 
the number in any order in the minuend is smaller 
than the number of the same order in the subtrahend 
the subtraction is performed by first reducing one 
unit of the next higher order to units of this lower 
order, and then taking away the number in the sub- 
trahend from all the units of that order. 

If necessary, other problems may be solved in 
this concrete way. Then the further work will con- 
sist in having the pupils to solve problems gradually 
increasing in length and difficulty, and the learning of 
the terms employed in problems in subtraction. 
These terms may be taught inductively, and will be so 
taught in work of the best kind. 

It is worthy of note that, if subtraction be taught 
in this rational manner, there arises no necessity for 



METHOD IN READING AND NUMBER. 159 

introducing the fiction of "borrowing and paying 
back." 

The Formal Process of Multiplication. — As in the 
formal process of addition, and subtraction, the pupil 
should now be well prepared for multiplication as a 
formal process, since he has been solving little prob- 
lems in multiplication for some three years. 

There are in this work also two stages, as fol- 
lows : 

1. That stage in which problems whose multi- 
plier consists of but one order are solved. 

2. That stage in which problems whose multi- 
plier consists of more than one order are solved. 

The First Stage. — This stage offers very little, if 
any, trouble in teaching, if the work up to this place 
has been reasonably well done. The following is a 
very good way to proceed in teaching it : 

Ask the child to write 125 on the board and write 
7 ones under it and draw a line beneath. Ask him 
how many 7x5 are, and have him write the result in 
the proper order. Then have him write the result of 
7x2 in the proper order; then, the result of 7x1 in 
the proper order. At this stage of the work the form 
is : 125 

7_ 

35 
140 

700 

Now, ask how the result may be written so as to 
appear as one number. If he can not see, he will 



160 METHOD IN READING AND NUMBER. 

have to be shown, since the form is purely a matter of 
convenience. 

Further work on more difficult problems is then 
to be given. 

The learner should also understand that a prob- 
lem of this kind is a problem in multiplication. 

The Second Stage. — This phase offers some points 
of difficulty in teaching, but will not be very difficult 
if the work as indicated in these studies has been 
done moderately well up to this place. The method 
of teaching is as follows : 

Ask the pupil to multiply, for instance, 236 by 24. 
He will probably not see how to multiply by so large 
a number. Lead him to see that he can multiply by 
4. This he will readily do since it is like the work he 
has been doing in the first stage of multiplication. 
Next he is to be led to see how to multiply by the 2 
tens. He knows that 2x6 = 12, but he must see that 
it is 12 tens. This he will see when he is led to see 
that 2 tens times 6 ones is 12 tens. He is told to write 
the 12 tens where it belongs. Let him fiU out onesr' 
place with a naught. The next step is to lead him to 
see that 3 tens multiplied by 2 tens gives 6 hundreds. 
Let him write the product where it belongs and fill 
out the places with naughts. And lastly he must be 
led to see that 2 hundreds multiplied by 2 tens gives 
4 thousands. Let him write the result again where it 
belongs and till out with naughts. Now he is to be 
led to see that to £:et the numbers all tosrether in the 



METHOD IN READING AND NUMBER. 161 

product he must add. The form of the above solution 

is as follows : 

236 
24 

944 
120 

600 

4000 

5664 

The next step is to lead the pupil to see how to 

shorten the form by writing as one number 120, 600, 

and 4000 and that in this case it is not necessary to 

write the naught in ones' place, since we can teU what 

the 2 is by its being under 4 tens. So the form is 

shortened to the following : 

236 
24 

944 

472 



5664 

The learner will usually catch the idea from the 
first problem. Then the further work consists of the 
solution of problems of various numbers gradually 
increasing in difficulty. From the above the teacher 
should see how to teach such problems as 876x40, 
and 8002 X 402. No new principles are involved. 

The Formal Process of Division. — There are two 
stages in teaching the formal process of division : 

1. What is commonly called long division. 

2. What is usually called short division. 

The Order of the Stages,^— Thev^ 13 ^ome difference 



162 METHOD IN READING AND NUMBER. 

of opinion as to which should be taught first, long 
division or short division. There are, no doubt, suc- 
cessful teachers who begin with short division and 
also successful teachers who begin with long division. 

It may be said truthfully that any abridged form 
is usually more difficult than the full form for any 
process. Now short division is an abridged form and 
should therefore properly come after the full form is 
known. It probably makes long division more diffi- 
cult for children, to teach short division first. 

Tlie First Stage. — After the learner has had the 
work up to this place as indicated in these studies he 
should be in such an attitude that he will want to see 
the reason for each step in any problem. The formal 
process should be taught in harmony with this idea. 
The method of teaching is somewhat as follows : 

Place on the board for instance, 456 and place the 
divisor 3 in its position, and tell the pupil you want to 
find how many threes in 456. Ask how many threes 
in 4. Wlien the pupil says 1, tell him where you will 
place it, and put it there. Now he must be led to see 
that 4 is four hundreds and so the 1 is one hundred. 
Ask him to show that the 1 is one hundred, and place 
the two naughts to the right. Then the pupil will 
have to be shown that the 3 is multiplied by 100 and 
the product written under 456, and then subtracted 
from it. The teacher now asks the child if there ar^ 
any 100 threes in 156. The next step is to lead the 
child to give the number of threes in 15, and to see 



METHOD IN READING AND NUMBER. 163 

that the 5 is 5 tens. Then multiply across and sub- 
tract. Lead him to see that the threes in 6 are 2 of 
ones order. The form now stands as follows : 

3)456(100 
300 50 

156 2 
150 



6 
6 
Now ask the pupil how many threes in 456, and 
lead him to see how the quotient may be written as 
one number. 

Tell him this is called a problem in division. Now 
give him a small problem to solve, for instance, 32-4-2. 
Lead him to give reasons for each step. Have him to 
solve many problems increasing in difficulty. When 
he begins to get skillful to some extent show him how 
the form, is further shortened by, instead of writing 
the two naughts at the right of the 3, just the three is 
written under hundreds and that the same is true of 
15, and that the 5 and the 6 are brought down only as 
needed. The shortened form is then as follows : 

3)456(152 
3 

15 
15 

6 
6 
Now give the learner problems gradually increas- 
ing in difficulty to solve according to the shorter form. 
The Second Stage, — The teaching of short division 



164 METHOD IN READING AND NUMBER. 

will now be very easy. It is evident that it is only a 
further shortening of the form. Using the same 
problem, for example, show the learner how the form 
may be further shortened into short division in the 
case of easy problems. Then give him plenty of suit- 
able problems to solve by the shortest form, and all 
will be well. 

Conclusion. — After having mastered the four fun- 
damental processes, the child is ready to study the 
various applications of these in the arithmetic work 
proper. 

It is beyond the scope of these studies to investi- 
gate the method of teaching these various applications. 
One or two general principles may be laid down how- 
ever, to guide in this work. 

The relations among the various arithmetical proc- 
esses should ahvays be made plain, and emphasized. For 
example, if in beginning addition of denominate num- 
bers it is shown that not a new principle is involved ; 
that it was all learned in addition of simple numbers, 
the whole subject at once becomes clear. 

2. In the solution of any problem the pupil should 
always be led to see just ivhat is given and what is to be 
found, before attempting the solution. 



CHAPTER XII. 

THE SUBJECT-MATTER AND PURPOSE OP NUMBER. 

General Nature of Subject- Matter. — It will be re- 
membered that subject-matter in any subject consists 
(1) of the facts in the subject, and (2) of the relations 
among those facts peculiar to that subject alone. 

Accordingly we can say that the subject-matter of 
number is, in general„the facts a iJu^M must learn, to 
Tcnow number, together with the proper relations of these 
facts to each other. 

A closer study here will show ( 1 ) what these facts 
of number are, and (2) what the relations in which 
they are to be considered are. The facts to be mas- 
tered in number study are the number series, or the 
number continuum. That is to say, the facts to be 
mastered in the study of number are the numbers 
from one to infinity. The number continuum, or the 
number series, consists of the numbers from one on, 
including one, of course. 

And the relations in which these numbers are to 
be studied are those indicated in our previous study. 
They are : 

1. The numbers as wholes. 

2. The numbers as to what they are made up of 
and ivhat they may be separated into. 



166 METHOD IN READING A^fD NUMBEIt. 

3. The numbers as to their notation. 

4. The numbers as to their denominate and gen- 
eral apjylications. 

From the above we get the following definite 
statement for the subject-matter of number: Tlte 
subject-matter of 7iumber is the numbers in the number 
Gontinmtm each (1) as a ivhole; {2) as to its notation; (3) 
as to ivJiat it is made up of and what it may be separated 
into, and (4^) as to its denominate and general applica- 
tions. 

The Purpose of Number. — It will be remembered 
that the purpose of any subject is to be determined 
from the effect the pursuit of that subject has on the 
mind. Now the pursuit of number as a subject, like 
the pursuit of any other subject, affects the mind in 
two general ways, as follows : 

1. By the pursuit of number the pupil gets 
knowledge valuable for guidance in living. This is 
called the knowledge-giving purpose. 

2. The pupil's mind gets exercise, and by means 
of this exercise the mind grows in ability to think 
accurately and readily. This is the disciplinary pur- 
pose of the study of number. 

The Knoivledge- giving Purpose. — Some subjects 
hold their places in the school curriculum because of 
their knowledge-giving value mainly, while others 
hold their places in the school curriculum because of 
their disciplinary value mainly. Number is a subject 
in the school curriculum mainly because its pursuit 



Method in reading and number. 167 

gives useful knowledge. This knowledge is such that 
it gives the learner the ability to grasp definitely a 
world of quantity that would otherwise remain a 
vague whole to him. Thus a knowledge of number 
gives guidance wherever the mind has occasion to 
measure any kind of quantity. Occasion arises 
mainly for the measure of quantity in one's business, 
or industrial, life and in the pursuit of some of the 
sciences. 

The Guidance a Knoiuledge of Nurnber Gives. — As 
just indicated a knowledge of number gives guidance 
in the industrial life of a people and in the develop- 
ment of some of the sciences. 

It helps here for us to consider what people who 
are engaged in industrial life do. They are chiefly 
employed in the following three lines : 

1. The production of commodities. 

2. The preparation of commodities. 

3. The distribution of commodities. 

By production of commodities is meant the pro- 
duction of corn, wheat, oats, barley, hay, cattle, hogs, 
poultry, wool, flax, hemp, fruit, cotton, coal, stone, 
iron, silk, etc. 

By preparation of commodities is mainly meant 
the manufacture of such things as can better be used 
in some other form than the original. 

Distribution of commodities means the process 
of sending them from place to place — to the points of 
consumption. 



168 METHOD IN READING AND NUMBER. 

A knowledge of number does not give a very great 
amount of guidance in the first line of these activi- 
ties — the production of commodities. However it 
gives some. The seasons of the year are to be noted, 
and measurements of time, etc., are to be made. A 
knowledge of number guides in all these things. 

The preparation of commodities would simply be 
an impossibility without the guidance which a knowl- 
edge of number furnishes. In preparing products 
constant need of measurement arises. The machin- 
ery employed in manufacture, on the farm, and in 
mines, etc., could never be made without the meas- 
urement of quantity. A knowledge of number alone 
furnishes guidance in these measurements. 

In the distribution of commodities a knowledge 
of number again furnishes much guidance. Things 
can not be distributed without the exchange of com- 
modities. And in exchange the need for the meas- 
urement of quantity is constant. There could be no 
traffic, no buying or selling without measurement of 
quantity. The knowledge of number furnishes guid- 
ance in all kinds of exchange. 

The distribution of things requires railroads and 
their equipments, steamboats, steamships, the dredg- 
ing of rivers, docks, canals, etc. , none of which can be 
made without the guidance the knowledge of number 
gives in measuring quantity. 

In the sciences of astronomy, physics, chemistry, 
geology, etc., a knowledge of number is constantly 



METHOD IN HEADING AND NUMBER. 169 

needed. It is safe to say that the natural sciences 
could never have reached the degree of development 
to which they have attained v^ithout a knowledge of 
number having supplemented them. 

This study should realize to us that, when it is 
said that the main purpose of nuiiiber is to give the child 
Jcnoioledge which luill enable him to make a vagioe lohole 
of quantity definite in his effort to think the external 
loorld, the statement is much more comprehensive 
than one would at first suppose. 

The Disciplinary Purpose. — While the disciplinarj^ 
value of the study of number is considerable, it is now 
believed that it has been overestimated. The follow- 
ing from W. T. Harris will indicate something of this 
thought : 

" The true psychological theory of number is the 
panacea for that exaggeration of the importance of 
arithmetic which prevails in our elementary schools. 
As if it were not enough that the science of number 
is indispensible for the conquest of Nature in time 
and space, these qualitative-unit teachers make the 
mistake of supposing that arithmetic deals with spir- 
itual being as much as with matter ; they confound 
quality with quantity, and consequently mathematics 
with metaphysics. Mental arithmetic becomes in 
their psychology 'the discipline for pure reason', 
although as a matter of fact the three figures of the 
regular syllogism are neither of them employed in 
mathematical reasoning." 



170 METHOD IN READING AND NUMBER. 

The study of number gives exercise in memory, 
imagination and reasoning. It is not particularly 
good to develop the memory or the imagination, but 
it is said to be most excellent to cultivate reasoning. 

Now it is true that the study of number develops 
reasoning, but it is worth while to inquire what kind 
of reasoning. Number study cultivates mathemat- 
ical, or necessary, reasoning, but the reasoning the 
learner will need most in life is not of this kind . The 
learner will need the kind of reasoning developed by 
the study of the natural sciences, history, and litera- 
ture — probable reasoning — much more than mathe- 
matical, or necessary, reasoning. 

It is certainly true that the value of mathematics 
from a disciplinary view point has been overestimated. 

Conclusions. — Our study of the purpose of num- 
ber leads to the following conclusions: 

1. The knowledge-giving purpose is the main 
purpose of number study. 

2. The knowledge-giving purpose is, to endow 
the learner with knowledge which will give guidance 
in making a vague whole of quantity definite in his 
effort to think Nature in time and space. 

3. That this is an entirely sufficient reason for 
studying number. 

4. That while the study of number gives mental 
discipline, its value from this point of view is com- 
monly overestimated. 



CHAPTER XIII. 

COMMON ERRORS IN TEACHING NUMBER. 

Prevalence of. — Number teaching offers opportu- 
nities for many errors in teaching, and since so many 
of the teachers in our primary schools begin teach- 
ing without having studied the method of teaching 
number, many flagrant errors are, no doubt, made in 
the work as commonly done. Some of these errors 
will be enumerated and studied because of the help 
that comes from such study. The following are some 
of these errors : 

1. Children are taught the wrong conception of 
number. 

2. Figures are taught instead of number. 

3. Number is taught in an unorganized, unsys- 
tematic, purposeless way. 

4. The formal processes of addition, subtraction, 
multiplication, and division are taught too early, and 
too much from the formal side. 

5. Children are not properly led to picture the 
conditions of problems before attempting to solve 
them. 

6. Too much formal drill is done on one number 
in the effort to exhaust it before taking up others. 



172 METHOD IN READING AND NUMBER. 

7. Tlie relations among the various topics in 
number are not suflSciently brought out and empha- 
sized. 

Wrong Number Concej^ts. — It is fair to say that 
more than seventy-five per cent, of persons who have 
studied number for years either have no definite idea 
of number or have a wrong idea of what number is. 
Perhaps the two wrong notions of number most gen- 
erally held are (1) that number is a quality of objects ; 
and (2) that the symbols of number — the figures — are 
the numbers. These two concepts of number are got 
by children because of the kind of teaching that is 
done. 

The kind of teaching that gives children the first 
one of these wrong number ideas is that which starts 
by having the child to closely observe some one thing 
in order that he may have the idea of one: and to 
closely look at another one thing in order that the idea 
two may arise in mind ; and so with the ideas three, 
four, Jive, etc. 

The kind of teaching from which children get the 
second one of these erroneous number ideas is that of 
dealing with figures from the first. The plan by 
which children are given little problems to solve on 
the board or on slates or on note books in the early 
work is almost sure to give children this idea of num- 
ber. Such problems as the following do this thing 
for children: 2+3, 4—2, 6-- 3, 4—3, 2+2, and 4--2. 

Figures instead of Number. — One author says the 



METHOD IN READING AND NUMBER. 173 

following on this point : "The fundamental defect in 
dealing with arithmetic is that expression is treated 
instead of number. Symbol is taught instead of sub- 
stance. " 

Dealing with figures instead of numbers is formal 
in the extreme and places the mind's emphasis wholly 
upon the symbol without its being made clear to the^ 
child what is symbolized. It is like his learning to 
repeat words without knowing their meaning. It is 
the kind of work that wholly fails to call forth the nat- 
ural activity of the mind in learning number. Work 
of this kind — dealing with symbols without getting 
their meaning — is the mental food which gives intel- 
lectual dyspepsia. 

Unsystematic Number Teaching. — Much number 
teaching in the past and some of it even in the 
present has been and is almost useless because of its 
unsystematic, fragmentary character. Teachers have 
oftentimes not known what the child can do in num- 
ber, what he knows of number when he comes to 
school, nor when and why he should begin number 
work; in short, they have had no systematic plan 
thought out to pursue in teaching number. This con- 
dition of things must be more or less common when 
so many of the teachers of the country attempt to 
teach number without having studied its method. 
And it will certainly continue to exist so long as there 
are so many teachers who either do not have the 
opportunity to study method in number ov do not 
appreciate the necessity of studying it, 



174 METHOD IN READING AND NUMBER. 

The evil of such fragmentary, scrappy work in 
number is that it is more or less purposeless; it 
wastes time and energy; it does not discriminate 
between the important and the unimportant; it is 
uninteresting and gives the pupils undesirable habits 
of thought. 

Teaching the Fundamental Processes front the Form 
Side. — The formal processes of addition, subtraction, 
multiplication, and division are not without reason. 
The form in addition and the others is founded on 
thought, but so often to the pupil as usually taught 
the form is purely without reason. Pupils who are 
sufficiently developed to study these formal processes 
may be led to see the reason for each step, and they 
should by all means be taught so they may do so. 
Teaching the formal processes of addition, subtrac- 
tion, multiplication, and division as mere form is re- 
sponsible for the senseless jargon of "carrying to the 
next higher order" in addition, and of ''borrowing 
one from the next higher order" in subtraction. 

The formal, meaningless manner in which the 
formal processes of addition, subtraction, multiplica- 
tion, and division have been taught, and are still 
taught is one of the worst errors, in my judgment, 
common in number teaching. 

Failure to Lead Children to Picture Problems. — There 
is no way for children to solve intelligently many 
problems which come up for solution except by pict- 
uring the problems. Children make ludicrous mis- 



METHOD IN READING AND NUMBER. l'75 

takes in their number work because of a failure to 
picture their problems. A child solved the problem, 
"If 2 men can build a fence in 10 days, how long will 
it take one man to build it?" as follows : "If two men 
can build the fence in ten days, one man can build the 
fence in one-half of ten days, or in five days." No 
child who pictured the problem would ever make such 
a blunder. If children are to be led to see just what 
is given and just what is to be found, and no child 
should ever solve a problem without doing so, they 
must be led into the habit of picturing the conditions 
of their problems. The advantage in such work is 
that it promotes clear, accurate, ready habits of 
thought. 

Exhausting a Number.— The habit of taking up one 
number, for instance 4, and just "wearing it out" 
before doing any work with the succeeding number is 
condemned by some of our foremost educators in the 
strongest terms. To keep the learner so long on one 
number is not only uninteresting and monotonous but 
is positively injurious to the child. It results in ar- 
rested development, and gives him a dislike for the 
subject of number. It is certainly in direct violation 
to the mind's natural action in learning number. 

Relations among Topics.— li> is quite customary for 
teachers to teach the various topics, as division, ratio, 
fractions, addition and subtraction of simple num- 
bers, addition and subtraction of compound numbers, 
etc., as isolated. This is a grave error, for thinking 



176 METHOD IN READING AND NUMBER. 

mathematically is only comparing numbers and proc- 
esses and discovering their likenesses and differ- 
ences; that is, tracing out relations. Nothing else 
so well reveals the nature of the various topics in 
number work as to compare them, and trace out the 
relations among them. A failure to do this results in 
the student's failure to see number as an organic 
whole. He rather gets the idea that the various topics 
are not essentially related. 

Thoughts of Others. — A careful study of the follow- 
ing quotation from McLellan and Dewey's Psychology 
of Number will well pay any student of method in 
number: 

"Since then, the natural action of the child's mind 
in gaining his first ideas of number is attended with 
interest, it seems clear that when under the formal 
teaching of number that interest, instead of being 
quickened and strengthened, actually dies out, the 
method of teaching must be seriously at fault. The 
method must lack the essentials of true method. It 
does not stimulate and cooperate with the rythmic 
movement of the mind, but rather impedes and prob- 
ably distorts it. The natural instinct of number, 
which is present in every one, is not guided by proper 
methods till effective development is reached. The 
native aptitude for number is continually baffled, and 
an artificial activity, opposed to all rational develop- 
ment of numerical ideas, is forced upon the mind. 
From this irrational process an arrested development 



METHOD IN READING AND NUMBER. 177 

of the number function ensues. An actual distaste 
for number is created ; the child is adjudged to have 
no interest in number and no taste for mathematics ; 
and to nature is ascribed an incapacity which is solely 
due to irrational instruction. It is perhaps not too 
much to say that nine-tenths of those who dislike 
arithmetic, or who at least feel that they have no apti- 
tude for mathematics, owe this misfortune to wrong 
teaching at first ; to a method which, instead of work- 
ing in harmony with the number instinct and so mak- 
ing every stage of development a preparation for the 
next, actually thwarts the natural movement of the 
mind, and substitutes for its spontaneous and free 
activity a forced and mechanical action accompanied 
with no vital interest, and leading neither to acquired 
knowledge or developed power. " 

"Avoid what has been called the 'fixed-unit' 
method. No greater mistake can be made than to 
begin with a single thing and to proceed by aggre- 
gating such independent wholes. The method works 
by fixed and isolated unities towards an undefined 
limit ; that is, it attempts to develop accurate ideas of 
quantity without the presence of that which is the 
essence of quantity— namely, the idea of limit. It 
does not promote, but actually warps, the natural 
action of the mind in its construction of number ; it 
leaves the fundamental numerical operations mean- 
ingless, and fractions a frowning hill of difficulty. 
No amount of questioning upon one thing in the vain 



178 METHOD IN READING AND NUMBER. 

attempt to develop the idea of 'one', no amount of drill 
on two such things or three such things, no amount 
of artificial analysis on the numbers from one to five, 
can make good the ineradicable defects of a beginning 
which actually obstructs the primary mental func- 
tions, and all but stifles the number instinct. 

Avoid, then, excessive analysis, the necessary 
consequence of this ' rigid unit ' method. This analy- 
sis, making appeals to an undeveloped power of nu- 
merical abstraction, becomes as dull and mechanical 
and quite as mischievous in its effects as the 'figure 
system ', which is considered but little better than a 
mere jugglery with number symbols. 

Avoid the error of assuming that there are exact 
numerical ideas in the mind as a result of a number 
of things before the senses. This ignores the fact 
that number is not a thing, not a property nor percep- 
tion of things, but the result of the mind's action in 
dealing with quantity. Avoid treating number as 
a series of separate and independent entities, each of 
which is to be thoroughly mastered before the next is 
taken up. Too much thoroughness in primary num- 
ber work is as harmful as too little thoroughness 
in advanced work. 

Avoid on the one hand the simultaneous teaching 
of the fundamental operations, and on the other hand 
the teaching which fails to recognize their logical and 
psychological connection. 

Avoid the error which makes the 'how many' 



METHOD IN READING AND NUMBER. 179 

alone constitute number, and leaves out of account the 
other coordinate factor 'how much '. The measuring 
idea must always be prominent in developing number 
and numerical operation. Without this idea of meas- 
urement no clear conception of number can be devel- 
oped, and the real meaning of the various operations 
as simply phases in the development of the measuring 
idea will never be grasped. 

Avoid the fallacy of assuming that the child, to 
know a number, must be able to picture all the num- 
bered units that make up a given quantity. 

Avoid the interest-killing monotony of the Grube 
grind on the three hundred and odd combinations of 
half a dozen numbers, which thus substitutes sheer 
mechanical action for the spontaneous activity that 
simultaneously develops numerical ideas and the 
power to retain them. " 

Conclusion. — In conclusion it may be repeated 
that the idea of measurement is to pervade and dom- 
inate the entire number work. This to the end that 
the child may grow unconsciously into right concep- 
tions of number and numerical operations. 



^^eT3-5 1901 



JAN 30 T907 



